growth rates for the linearized motion of fluid interfaces away from equilibrium we consider the motion of a two dimensional interface separating an inviscid incompressible irrotational fluid influenced by gravity from a region of zero density we show that under certain conditions the equations of motion linearized about a presumed time dependent solution are wellposed that is linear disturbances have a bounded rate of growth if surface tension is neglected the linear equations are well posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity similar to the criterion formulated by g i taylor if surface tension is included the linear equations are well posed without qualifications whether the fluid is above or below the interface an interesting qualitative structure is found for the linear equations a lagrangian approach is used like that of numerical work such as 3 except that the interface is assumed horizontal at infinity certain integral equations which occur involving double layer potentials are shown to be solvable in the present case 1993 john wiley sons inc

multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks we show that an n neuron cellular neural network with time varying delay can have 2n periodic orbits located in saturation regions and these periodic orbits are locally exponentially attractive in addition we give some conditions for ascertaining periodic orbits to be locally or globally exponentially attractive and allow them to locate in any designated region as a special case of exponential periodicity exponential stability of delayed cellular neural networks is also characterized these conditions improve and extend the existing results in the literature to illustrate and compare the results simulation results are discussed in three numerical examples

a new method for complete stability analysis of cellular neural networks with time delay this paper presents new complete stability results for delayed cellular neural networks dcnns a novel method is proposed for complete stability analysis of dcnns by applying the m matrix theory and introducing some new estimation techniques on the solutions of dcnns a simple and improved complete stability criterion is derived the new criterion unifies the delay dependent and delay independent complete stability conditions for dcnns moreover the obtained delay dependent criterion can give a larger upper bound of the time delay than the existing ones such that the complete stability can still be retained numerical examples are presented which show that the new complete stability results for dcnns are compared favorably with the existing results

splash singularity for water waves we exhibit smooth initial data for the two dimensional 2d water wave equation for which we prove that smoothness of the interface breaks down in finite time moreover we show a stability result together with numerical evidence that there exist solutions of the 2d water wave equation that start from a graph turn over and collapse in a splash singularity self intersecting curve in one point in finite time

systems with counterclockwise input output dynamics a new input output property is proposed suitable for the study of positive feedback interconnections both in a linear and nonlinear set up convergence results and small gain theorems are proved as well as criteria for the application of the property to the study of multistability lyapunov like conditions and dissipation inequalities for its detection are also provided

multistability and instability of neural networks with discontinuous nonmonotonic piecewise linear activation functions in this paper we discuss the coexistence and dynamical behaviors of multiple equilibrium points for recurrent neural networks with a class of discontinuous nonmonotonic piecewise linear activation functions it is proved that under some conditions such n neuron neural networks can have at least 5 n equilibrium points 3 n of which are locally stable and the others are unstable based on the contraction mapping theorem and the theory of strict diagonal dominance matrix the investigation shows that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibrium points and more locally stable equilibrium points than the ones with continuous mexican hat type activation function or discontinuous two level activation functions an illustrative example with computer simulations is presented to verify the theoretical analysis

impulsive stabilization and impulsive synchronization of discrete time delayed neural networks this paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete time delayed neural networks ddnns two types of ddnns with stabilizing impulses are studied by introducing the time varying lyapunov functional to capture the dynamical characteristics of discrete time impulsive delayed neural networks didnns and by using a convex combination technique new exponential stability criteria are derived in terms of linear matrix inequalities the stability criteria for didnns are independent of the size of time delay but rely on the lengths of impulsive intervals with the newly obtained stability results sufficient conditions on the existence of linear state feedback impulsive controllers are derived moreover a novel impulsive synchronization scheme for two identical ddnns is proposed the novel impulsive synchronization scheme allows synchronizing two identical ddnns with unknown delays simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of ddnns finally an application of the obtained impulsive synchronization result for two identical chaotic ddnns to a secure communication scheme is presented

multistability and multiperiodicity of delayed cohen grossberg neural networks with a general class of activation functions abstract in this paper by using analysis approach and decomposition of state space the multistability and multiperiodicity issues are discussed for cohen grossberg neural networks cgnns with time varying delays and a general class of activation functions where the general class of activation functions consist of nondecreasing functions with saturation s including piecewise linear functions with two corner points and standard activation functions as its special case based on the cauchy convergence principle some sufficient conditions are obtained for checking the existence and uniqueness of equilibrium points of the n neuron cgnns it is shown that the n neuron cgnns can have 2n locally exponentially stable equilibrium points located in saturation regions also some conditions are derived for ascertaining equilibrium points to be locally exponentially stable or globally exponentially attractive and to be located in any designated region as an extension of multistability some similar results are presented for ascertaining multiple periodic orbits when external inputs of the n neuron cgnns are periodic finally three examples are given to illustrate the effectiveness of the obtained results

well posedness in smooth function spaces for moving boundary 1 d compressible euler equations in physical vacuum we prove well posedness for the 3 d compressible euler equations with moving physical vacuum boundary with an equation of state given by the so called gamma gas law for gamma 1 the physical vacuum singularity requires the sound speed c to go to zero as the square root of the distance to the moving boundary and thus creates a degenerate and characteristic hyperbolic free boundary system wherein the density vanishes on the free boundary the uniform kreiss lopatinskii condition is violated and manifest derivative loss ensues nevertheless we are able to establish the existence of unique solutions to this system on a short time interval which are smooth in sobolev spaces all the way to the moving boundary and our estimates have no derivative loss with respect to initial data our proof is founded on an approximation of the euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term chosen to preserve as much of the geometric structure of the euler equations as possible we first construct solutions to this degenerate parabolic regularization using a new higher order hardy type inequality we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter solutions to the compressible euler equations are found in the limit as the artificial viscosity tends to zero our regular solutions can be viewed as degenerate viscosity solutions out methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws

multistability and convergence in delayed neural networks abstract we present the existence of 2 n stable stationary solutions for a general n dimensional delayed neural networks with several classes of activation functions the theory is obtained through formulating parameter conditions motivated by a geometrical observation positively invariant regions for the flows generated by the system and basins of attraction for these stationary solutions are established the theory is also extended to the existence of 2 n limit cycles for the n dimensional delayed neural networks with time periodic inputs it is further confirmed that quasiconvergence is generic for the networks through justifying the strongly order preserving property as the self feedback time lags are small for the neurons with negative self connection weights our theory on existence of multiple equilibria is then incorporated into this quasiconvergence for the network four numerical simulations are presented to illustrate our theory

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

impulsive multisynchronization of coupled multistable neural networks with time varying delay this paper studies the synchronization problem of coupled delayed multistable neural networks nns with directed topology to begin with several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points then two new concepts named dynamical multisynchronization dms and static multisynchronization sms are introduced to describe the two novel kinds of synchronization manifolds using the impulsive control strategy and the razumikhin type technique some sufficient conditions for both the dms and the sms of the controlled coupled delayed multistable nns with fixed and switching topologies are derived respectively simulation examples are presented to illustrate the effectiveness of the proposed results

global infinite energy solutions for the 2d gravity water waves system we prove global existence and a modified scattering property for the solutions of the 2d gravity water waves system in the infinite depth setting for a class of initial data which is only required to be small above the level h 1 5 h 1 5 1 2 no assumption is made below this level therefore the nonlinear solution can have infinite energy as a direct consequence the momentum condition assumed on the physical velocity in all previous small energy results by ionescu pusateri alazard delort and ifrim tataru is removed 2017 wiley periodicals inc

stability analysis of continuous time and discrete time quaternion valued neural networks with linear threshold neurons this paper addresses the problem of stability for continuous time and discrete time quaternion valued neural networks qvnns with linear threshold neurons applying the semidiscretization technique to the continuous time qvnns the discrete time analogs are obtained which preserve the dynamical characteristics of their continuous time counterparts via the plural decomposition method of quaternion homeomorphic mapping theorem as well as lyapunov theorem some sufficient conditions on the existence uniqueness and global asymptotical stability of the equilibrium point are derived for the continuous time qvnns and their discrete time analogs respectively furthermore a uniform sufficient condition on the existence uniqueness and global asymptotical stability of the equilibrium point is obtained for both continuous time qvnns and their discrete time version finally two numerical examples are provided to substantiate the effectiveness of the proposed results

multistability of neural networks with time varying delays and concave convex characteristics in this paper stability of multiple equilibria of neural networks with time varying delays and concave convex characteristics is formulated and studied some sufficient conditions are obtained to ensure that an n neuron neural network with concave convex characteristics can have a fixed point located in the appointed region by means of an appropriate partition of the n dimensional state space when nonlinear activation functions of an n neuron neural network are concave or convex in 2k 2m 1 intervals this neural network can have 2k 2m 1 n equilibrium points this result can be applied to the multiobjective optimal control and associative memory in particular several succinct criteria are given to ascertain multistability of cellular neural networks these stability conditions are the improvement and extension of the existing stability results in the literature a numerical example is given to illustrate the theoretical findings via computer simulations

bogdanov takens singularity in tri neuron network with time delay this brief reports a retarded functional differential equation modeling tri neuron network with time delay the bogdanov takens b t bifurcation is investigated by using the center manifold reduction and the normal form method we get the versal unfolding of the norm forms at the b t singularity and show that the model can exhibit pitchfork hopf homoclinic and double limit cycles bifurcations some numerical simulations are given to support the analytic results and explore chaotic dynamics finally an algorithm is given to show that chaotic tri neuron networks can be used for encrypting a color image

finite time singularities for the free boundary incompressible euler equations in this paper we prove the existence of smooth initial data for the 2d free boundary incompressible euler equations also known for some particular scenarios as the water wave problem for which the smoothness of the interface breaks down in nite time into a splash singularity or a splat singularity

robust stability analysis for interval cohen grossberg neural networks with unknown time varying delays in this paper robust stability problems for interval cohen grossberg neural networks with unknown time varying delays are investigated using linear matrix inequality m matrix theory and halanay inequality techniques new sufficient conditions independent of time varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval cohen grossberg neural networks with time varying delays all these results have no restriction on the rate of change of the time varying delays compared to some existing results these new criteria are less conservative and are more convenient to check two numerical examples are used to show the effectiveness of the present results

energy estimates and local well posedness of 3d interfacial hydroelastic waves between two incompressible fluids abstract in the current paper we are concerned with waves propagating through the deformation of a thin elastic sheet between two incompressible and inviscid fluids which are usually called hydroelastic waves in the literature to model deformable sheets interacting with surrounding fluids the main purpose of the present study is to solve a basic question on the theoretical side i e the local well posedness issue the problem is formulated by the full euler equations without the assumption of irrotationality for fluids combined with the plotnikov toland model for the elastic sheet based on geometric considerations we derive energy estimates and prove the local existence and uniqueness of solution for this system in n 2 dimensions even if velocity fields are rotational

multistability of complex valued recurrent neural networks with real imaginary type activation functions this paper addresses the multistability problem of n dimensional complex valued recurrent neural networks with real imaginary type activation functions sufficient conditions are proposed for checking the existence of 2 1 2 1 n 1 equilibria under these conditions 1 1 n equilibria are locally exponentially stable and the others are unstable attractive basins of equilibria are also investigated complete attractive basins of equilibria in 1 dimensional complex valued recurrent neural networks are obtained the obtained stability results improve and extend the existing ones two numerical examples are given to illustrate the effectiveness of the obtained results

turning waves and breakdown for incompressible flows we consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids specifically we study the muskat and water wave problems we show that starting with a family of initial data given by f0 the interface reaches a regime in finite time in which is no longer a graph therefore there exists a time t where the solution of the free boundary problem parameterized as f t blows up f l t in particular for the muskat problem this result allows us to reach an unstable regime for which the rayleigh taylor condition changes sign and the solution breaks down

stability and synchronization of discrete time neural networks with switching parameters and time varying delays this paper is concerned with the problems of exponential stability analysis and synchronization of discrete time switched delayed neural networks using the average dwell time approach together with the piecewise lyapunov function technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time delays benefitting from the delay partitioning method and the free weighting matrix technique the conservatism of the obtained results is reduced in addition the decay estimates are explicitly given and the synchronization problem is solved the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

multistability and multiperiodicity of delayed bidirectional associative memory neural networks with discontinuous activation functions abstract in this paper the multistability and multiperiodicity issues are discussed for 2 n dimensional delayed bidirectional associative memory neural networks with r level discontinuous activation functions sufficient conditions are established to ensure the existence of r n locally exponentially stable equilibria as an extension of multistability conditions are established to ensure the existence of r n locally exponentially stable periodic solutions when external inputs are periodic finally two examples are given to illustrate the effectiveness of the obtained results

multistability of clustered states in a globally inhibitory network abstract we study a network of m identical excitatory cells projecting excitatory synaptic connections onto a single inhibitory interneuron which is reciprocally coupled to all excitatory cells through inhibitory synapses possessing short term synaptic depression we find that such a network with global inhibition possesses multiple stable activity patterns with distinct periods characterized by the clustering of the excitatory cells into synchronized sub populations we prove the existence and stability of n cluster solutions in a m cell network using methods of geometric singular perturbation theory we show that any n cluster solution must satisfy a set of consistency conditions that can be geometrically derived we then characterize the basin of attraction of each solution although frequency dependent depression is not necessary for multistability we discuss how it plays a key role in determining network behavior we find a functional relationship between the level of synaptic depression the number of clusters and the interspike interval between neurons this relationship is much less pronounced in the absence of depression implications for temporal coding and memory storage are discussed

well posedness for the motion of an incompressible liquid with free surface boundary we study the motion of an incompressible perfect liquid body in vacuum this can be thought of as a model for the motion of the ocean or a star the free surface moves with the velocity of the liquid and the pressure vanishes on the free surface this leads to a free boundary problem for euler s equations where the regularity of the boundary enters to highest order we prove local existence in sobolev spaces assuming a physical condition related to the fact that the pressure of a fluid has to be positive

on the absence of splash singularities in the case of two fluid interfaces we show that splash singularities cannot develop in the case of locally smooth solutions of the two fluid interfaces in two dimensions more precisely we show that the scenario of formation of singularities discovered by castro cordoba fefferman gancedo gomez serrano 6 in the case of the water waves system in which the interface remains locally smooth but self intersects in finite time is completely prevented in the case of two fluid interfaces with positive densities

multistability of two kinds of recurrent neural networks with activation functions symmetrical about the origin on the phase plane in this paper we investigate multistability of two kinds of recurrent neural networks with time varying delays and activation functions symmetrical about the origin on the phase plane one kind of activation function is with zero slope at the origin on the phase plane while the other is with nonzero slope at the origin on the phase plane we derive sufficient conditions under which these two kinds of n dimensional recurrent neural networks are guaranteed to have 2m 1 n equilibrium points with m 1 n of them being locally exponentially stable these new conditions improve and extend the existing multistability results for recurrent neural networks finally the validity and performance of the theoretical results are demonstrated through two numerical examples

multistability for delayed neural networks via sequential contracting in this paper we explore a variety of new multistability scenarios in the general delayed neural network system geometric structure embedded in equations is exploited and incorporated into the analysis to elucidate the underlying dynamics criteria derived from different geometric configurations lead to disparate numbers of equilibria a new approach named sequential contracting is applied to conclude the global convergence to multiple equilibrium points of the system the formulation accommodates both smooth sigmoidal and piecewise linear activation functions several numerical examples illustrate the present analytic theory

on the cauchy problem for gravity water waves we are interested in the system of gravity water waves equations without surface tension our purpose is to study the optimal regularity thresholds for the initial conditions in terms of sobolev embeddings the initial surfaces we consider turn out to be only of c 3 2 epsilon class for some epsilon 0 and consequently have unbounded curvature while the initial velocities are only lipschitz we reduce the system using a paradifferential approach

control of multistate hopping intermittency in multistable regimes noise can create multistate hopping intermittency i e intermittent transitions among coexisting stable attractors we demonstrate that a small periodic perturbation can significantly control such hopping intermittency by control we imply a qualitative change in the probability distribution of occupation in the phase space around the stable attractors in other words if the uncontrolled system exhibits a preference to stay around a given attractor say a in comparison to another attractor say b the control perturbation creates a contrasting scenario so that attractor b is most frequently visited and consequently the occupation probability becomes maximum around b instead of a the control perturbation works in the following way it destroys attractor a by boundary crisis while attractor b remains stable as a result even if the system is pushed by noise into the erstwhile basin of attractor a the system does not remain there for long and therefore stays longer around attractor b significantly such a change in the intermittent scenario can be obtained by a small amplitude and slow periodic perturbation the control is theoretically demonstrated with two standard models namely lorenz equations for autonomous systems and the periodically driven damped toda oscillator for nonautonomous systems recent experiments with a cavity loss modulated mathrm c mathrm o 2 laser and an analog circuit of lorenz equations have validated our theoretical demonstrations excellently

the free boundary euler equations with large surface tension abstract we study the free boundary euler equations with surface tension in three spatial dimensions showing that the equations are well posed if the coefficient of surface tension is positive then we prove that under natural assumptions the solutions of the free boundary motion converge to solutions of the euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity

well posedness in smooth function spaces for the moving boundary three dimensional compressible euler equations in physical vacuum we prove well posedness for the three dimensional compressible euler equations with moving physical vacuum boundary with an equation of state given by p c for 1 the physical vacuum singularity requires the sound speed c to go to zero as the square root of the distance to the moving boundary and thus creates a degenerate and characteristic hyperbolic free boundary system wherein the density vanishes on the free boundary the uniform kreiss lopatinskii condition is violated and manifest derivative loss ensues nevertheless we are able to establish the existence of unique solutions to this system on a short time interval which are smooth in sobolev spaces all the way to the moving boundary and our estimates have no derivative loss with respect to initial data our proof is founded on an approximation of the euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term chosen to preserve as much of the geometric structure of the euler equations as possible we first construct solutions to this degenerate parabolic regularization using a higher order version of hardy s inequality we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter solutions to the compressible euler equations are found in the limit as the artificial viscosity tends to zero our regular solutions can be viewed as degenerate viscosity solutions our methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws

multistability of recurrent neural networks with time varying delays and the piecewise linear activation function in this brief stability of multiple equilibria of recurrent neural networks with time varying delays and the piecewise linear activation function is studied a sufficient condition is obtained to ensure that n neuron recurrent neural networks can have 4k 1 n equilibrium points and 2k n of them are locally exponentially stable this condition improves and extends the existing stability results in the literature simulation results are also discussed in one illustrative example

multistability and new attraction basins of almost periodic solutions of delayed neural networks in this paper we investigate multistability of almost periodic solutions of recurrently connected neural networks with delays simply called delayed neural networks we will reveal that under some conditions the space rn can be divided into 2n subsets and in each subset the delayed n neuron neural network has a locally stable almost periodic solution furthermore we also investigate the attraction basins of these almost periodic solutions we reveal that the attraction basin of almost periodic trajectory is larger than the subset where the corresponding almost periodic trajectory is located in addition several numerical simulations are presented to corroborate the theoretical results

a nonlinear control method based on anfis and multiple models for a class of siso nonlinear systems and its application this paper presents a novel nonlinear control strategy for a class of uncertain single input and single output discrete time nonlinear systems with unstable zero dynamics the proposed method combines adaptive network based fuzzy inference system anfis with multiple models where a linear robust controller an anfis based nonlinear controller and a switching mechanism are integrated using multiple models technique it has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system moreover it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance as a result the controller has the following three outstanding features compared with existing control strategies first this method relaxes the assumption of commonly used uniform boundedness on the unmodeled dynamics and thus enhances its applicability second since anfis is used to estimate and compensate the effect caused by the unmodeled dynamics the convergence rate of neural network learning has been increased third a one to one mapping technique is adapted to guarantee the universal approximation property of anfis the proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system respectively where its effectiveness has been justified

boundedness and complete stability of complex valued neural networks with time delay in this paper the boundedness and complete stability of complex valued neural networks cvnns with time delay are studied some conditions to guarantee the boundedness of the cvnns are derived using local inhibition moreover under the boundedness conditions a compact set that globally attracts all the trajectories of the network is also given additionally several conditions in terms of real valued linear matrix inequalities lmis for complete stability of the cvnns are established via the energy minimization method and the approach that converts the complex valued lmis to real valued ones examples with simulation results are given to show the effectiveness of the theoretical analysis

global regularity of 2d density patches for inhomogeneous navier stokes this paper is about lions open problem on density patches lions in mathematical topics in fluid mechanics vol 1 volume 3 of oxford lecture series in mathematics and its applications clarendon press oxford university press new york 1996 whether or not inhomogeneous incompressible navier stokes equations preserve the initial regularity of the free boundary given by density patches using classical sobolev spaces for the velocity we first establish the propagation of c 1 gamma regularity with 0 gamma 1 in the case of positive density furthermore we go beyond this to show the persistence of a geometrical quantity such as the curvature in addition we obtain a proof for c 2 gamma regularity

a finite difference time domain solution for three dimensional electromagnetic modeling we have developed a finite difference solution for three dimensional 3 d transient electromagnetic problems the solution steps maxwell s equations in time using a staggered grid technique the time stepping uses a modified version of the du fort frankel method which is explicit and always stable both conductivity and magnetic permeability can be functions of space and the model geometry can be arbitrarily complicated the solution provides both electric and magnetic field responses throughout the earth because it solves the coupled first order maxwell s equations the solution avoids approximating spatial derivatives of physical properties and thus overcomes many related numerical difficulties moreover since the divergence free condition for the magnetic field is incorporated explicitly the solution provides accurate results for the magnetic field at late times an inhomogeneous dirichlet boundary condition is imposed at the surface of the earth while a homogeneous dirichlet condition is employed along the subsurface boundaries numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth order difference method at early times and a second order method at other times numerical checks against analytical integral equation and spectral differential difference solutions show that the solution provides accurate results execution time for a typical model is about 3 5 hours on an ibm 3090 600s computer for computing the field to 10 ms that model contains 100 x 100 x 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry with the smallest grid spacing at 10 m and the highest resistivity at 100 omega m the execution time indicates that the solution is computer intensive but it is valuable in providing much needed insight about tem responses in complicated 3 d situations

multiple psi type stability of cohen grossberg neural networks with both time varying discrete delays and distributed delays in this paper multiple psi type stability of cohen grossberg neural networks cgnns with both time varying discrete delays and distributed delays is investigated by utilizing psi type functions combined with a new psi type integral inequality for treating distributed delay terms some sufficient conditions are obtained to ensure that multiple equilibrium points are psi type stable for cgnns with discrete and distributed delays where the distributed delays include bounded and unbounded delays these conditions of cgnns with different output functions are less restrictive more specifically the algebraic criteria of the generalized model are applicable to several well known neural network models by taking special parameters and multiple different output functions are introduced to replace some of the same output functions which improves the diversity of output results for the design of neural networks in addition the estimation of relative convergence rate of psi type stability is determined by the parameters of cgnns and the selection of psi type functions as a result the existing results on multistability and monostability can be improved and extended finally some numerical simulations are presented to illustrate the effectiveness of the obtained results

non splat singularity for the one phase muskat problem for the water waves equations the existence of splat singularities has been shown in 3 i e the interface self intersects along an arc in finite time the aim of this paper is to show the absence of splat singularities for the incompressible fluid dynamics in porous media

global robust stability criteria for interval delayed full range cellular neural networks this brief considers a class of delayed full range fr cellular neural networks cnns with uncertain interconnections between neurons modeled by means of intervalized matrices using mathematical tools from the theory of differential inclusions a fundamental result on global robust stability of standard s cnns is extended to prove global robust exponential stability for the corresponding class same interconnection weights and inputs of fr cnns the result is of theoretical interest since in general the equivalence between the dynamical behavior of fr cnns and s cnns is not guaranteed

multistability of discrete time recurrent neural networks with unsaturating piecewise linear activation functions this paper studies the multistability of a class of discrete time recurrent neural networks with unsaturating piecewise linear activation functions it addresses the nondivergence global attractivity and complete stability of the networks using the local inhibition conditions for nondivergence are derived which not only guarantee nondivergence but also allow for the existence of multiequilibrium points under these nondivergence conditions global attractive compact sets are obtained complete stability is studied via constructing novel energy functions and using the well known cauchy convergence principle examples and simulation results are used to illustrate the theory

on the motion of vortex sheets with surface tension in three dimensional euler equations with vorticity the motion of vortex sheets with surface tension has been analyzed in the setting of irrotational flows by ambrose 1 and ambrose and masmoudi 2 in two dimensions and by ambrose and masmoudi 3 in three dimensions with irrotationality the nonlinear euler equations reduce to poisson s equation for the pressure function in the bulk and the motion of the vortex sheet is decoupled from that of the fluid thus allowing boundary integral methods to be employed in a general flow with vorticity the full two phase euler equations must be analyzed in this instance the motion of the two phases of fluid is coupled to the motion of the vortex sheet and entirely new mathematical methods must be developed to obtain a well posedness theory in particular a new class of approximation schemes must be employed that preserve the transport type structure of the vorticity an issue that by definition does not arise either in the irrotational theory or in the analysis of the euler equations on fixed domains in the general case with vorticity present in the fluid the vortex sheet is a surface of discontinuity propagated by the fluid representing the material interface between two incompressible inviscid fluids with densities c and respectively the tangential velocity of the fluid suffers a jump discontinuity along the material interface leading to the well known kelvin helmholtz or rayleigh taylor instabilities when surface tension is neglected the velocity of the vortex sheet is the normal component of the fluid velocity whose continuity across the material interface t is enforced in addition to incompressibility the continuity of the normal rather than tangential component of velocity across t is a fundamental difference between vortex sheet evolution and multi d shock wave evolution

well posedness of the muskat problem with h2 initial data abstract we study the dynamics of the interface between two incompressible fluids in a two dimensional porous medium whose flow is modeled by the muskat equations for the two phase muskat problem we establish global well posedness and decay to equilibrium for small h 2 perturbations of the rest state for the one phase muskat problem we prove local well posedness for h 2 initial data of arbitrary size finally we show that solutions to the muskat equations instantaneously become infinitely smooth

global analysis of a model for capillary water waves in two dimensions in this paper we prove a global regularity result for a quadratic quasilinear model associated to the water waves system with surface tension and no gravity in dimension 2 the capillary waves system the model we consider here retains most of the difficulties of the full capillary water waves system including the delicate time resonance structure and modified scattering it is slightly simpler however at the technical level and our goal here is to present our method in this simplified situation the analysis of the full system is presented in a preprint by the authors 2014 2016 wiley periodicals inc

further result on guaranteed h_ infty performance state estimation of delayed static neural networks this brief considers the guaranteed h infty performance state estimation problem of delayed static neural networks an arcak type state estimator which is more general than the widely adopted luenberger type one is chosen to tackle this issue a delay dependent criterion is derived under which the estimation error system is globally asymptotically stable with a prescribed h infty performance it is shown that the design of suitable gain matrices and the optimal performance index are accomplished by solving a convex optimization problem subject to two linear matrix inequalities compared with some previous results much better performance is achieved by our approach which is greatly benefited from introducing an additional gain matrix in the domain of activation function an example is finally given to demonstrate the advantage of the developed result

rayleigh taylor breakdown for the muskat problem with applications to water waves the muskat problem models the evolution of the interface between two different fluids in porous media the rayleigh taylor condition is natural to reach linear stability of the muskat problem we show that the rayleigh taylor condition may hold initially but break down in finite time as a consequence of the method used we prove the existence of water waves turning

a hybrid three dimensional electromagnetic modeling scheme we present an efficient numerical method for computing electromagnetic em scattering of arbitrary three dimensional 3 d local inhomogeneities buried in a uniform or two layered earth in this scheme the inhomogeneity is enclosed by a volume whose conductivity is discretized by a finite element mesh and whose boundary is only a slight distance away from the inhomogeneity the scheme uses two sets of independent equations the first is a set of finite element equations derived from a variational integral and the second is a mathematical expression for the fields at the boundany in terms of electric fields inside the boundary the green s function is used to derive the second set of equations an iterative algorithm has been developed to solve these two sets of equations the solutions are the electric fields at nodes inside the finite element mesh the scattered fields anywhere may then be obtained by performing volume integrations over the inhomogeneous region the scheme is used for modeling 3 d inho

convergence in networks with counterclockwise neural dynamics the notion of counterclockwise ccw input output i o dynamics introduced by angeli 2006 to deal with questions of multistability in interconnected dynamical systems is applied and further developed in order to analyze convergence and stability of neural networks by pursuing a modular approach we interpret a cellular nonlinear network cnn as a positive feedback of a parallel block of single input single output siso dynamical systems the neurons and a static multiple input multiple output mimo system that couples them typically the so called interconnection matrix the analysis extends previously known results by enlarging the class of allowed neural dynamics to higher order neurons

the zero surface tension limit of two dimensional water waves we consider two dimensional water waves of infinite depth periodic in the horizontal direction it has been proven by wu in the slightly different nonperiodic setting that solutions to this initial value problem exist in the absence of surface tension recently ambrose has proven that solutions exist when surface tension is taken into account in this paper we provide a shorter more elementary proof of existence of solutions to the water wave initial value problem both with and without surface tension our proof requires estimating the growth of geometric quantities using a renormalized arc length parametrization of the free surface and using physical quantities related to the tangential velocity of the free surface using this formulation we find that as surface tension goes to 0 the water wave without surface tension is the limit of the water wave with surface tension far from being a simple adaptation of previous works our method requires a very original choice of variables these variables turn out to be physical and well adapted to both cases c

well posedness and decay to equilibrium for the muskat problem with discontinuous permeability we first prove local in time well posedness for the muskat problem modeling fluid flow in a two dimensional inhomogeneous porous media the permeability of the porous medium is described by a step function with a jump discontinuity across the fixed in time curve x 1 1 f x 1 while the interface separating the fluid from the vacuum region is given by the time dependent curve x 1 h x 1 t our estimates are based on a new methodology that relies upon a careful study of the pde system coupling darcy s law and incompressibility of the fluid rather than the analysis of the singular integral contour equation for the interface function h we are able to develop an existence theory for any initial interface given by h 0 in h 2 and any permeability curve of discontinuity that is given by f in h 2 5 in particular our method allows for both curves to have pointwise unbounded curvature in the case that the permeability discontinuity is the set f 0 we prove global existence and decay to equilibrium for small initial data this decay is obtained using a new energy energy dissipation inequality that couples tangential derivatives of the velocity in the bulk of the fluid with the curvature of the interface to the best of our knowledge this is the first global existence result for the muskat problem with discontinuous permeability

absence of splash singularities for surface quasi geostrophic sharp fronts and the muskat problem in this paper for both the sharp front surface quasi geostrophic equation and the muskat problem we rule out the splash singularity blow up scenario in other words we prove that the contours evolving from either of these systems cannot intersect at a single point while the free boundary remains smooth splash singularities have been shown to hold for the free boundary incompressible euler equation in the form of the water waves contour evolution problem our result confirms the numerical simulations in earlier work in which it was shown that the curvature blows up because the contours collapse at a point here we prove that maintaining control of the curvature will remove the possibility of pointwise interphase collapse another conclusion that we provide is a better understanding of earlier work in which squirt singularities are ruled out in this case a positive volume of fluid between the contours cannot be ejected in finite time

on the finite time splash and splat singularities for the 3 d free surface euler equations we prove that the 3 d free surface incompressible euler equations with regular initial geometries and velocity fields have solutions which can form a finite time splash or splat singularity first introduced in castro et al splash singularity for water waves http arxiv org abs 1106 2120v2 2011 wherein the evolving 2 d hypersurface the moving boundary of the fluid domain self intersects at a point or on surface such singularities can occur when the crest of a breaking wave falls unto its trough or in the study of drop impact upon liquid surfaces our approach is founded upon the lagrangian description of the free boundary problem combined with a novel approximation scheme of a finite collection of local coordinate charts as such we are able to analyze a rather general set of geometries for the evolving 2 d free surface of the fluid we do not assume the fluid is irrotational and as such our method can be used for a number of other fluid interface problems including compressible flows plasmas as well as the inclusion of surface tension effects

global wellposedness of the 3 d full water wave problem we consider the problem of global in time existence and uniqueness of solutions of the 3 d infinite depth full water wave problem in the setting that the interface tends to the horizontal plane the velocity and acceleration on the interface tend to zero at spatial infinity we show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders for any initial interface that is sufficiently small in its steepness and velocity we show that there exists a unique smooth solution of the full water wave problem for all time and the solution decays at the rate 1 t

on the existence of stationary splash singularities for the euler equations abstract in this paper we discuss the existence of stationary incompressible fluids with splash singularities specifically we show that there are stationary solutions to the euler equations with two fluids whose interfaces are arbitrarily close to a splash and that there are stationary water waves with splash singularities

numerical modeling of the electromagnetic response of three dimensional conductors in a layered earth this paper describes a numerical modeling program which was developed for computing the electromagnetic response of a three dimensional conductor in a layered earth the algorithm is a hybrid one in the sense that a finite element method is combined with an integral equation approach for the complete solution of the problem in this approach two relatively small matrices are inverted to obtain the secondary magnetic fields at the interior nodes of the subdivided volume the finite element method requires special attention at low frequencies i e when the body dimensions are small compared with the skin depth the method was tested with various models involving spheres and rectangular dikes and comparisons have been made with analytical numerical and scale modeling data these comparisons generally show good agreement between our numerical model and the other models tested examples are given which show the flexibility and usefulness of this modeling algorithm when applied to a ground or airborne prospecting system with a coil separation of 10 m

feasibility of simplified integral equation modeling of low frequency marine csem with a resistive target we have assessed the accuracy of a simplified integral equation sie modeling approach for marine controlled source electromagnetics csem with low applied frequencies and a resistive target the most computationally intensive part of rigorous integral equation ie modeling is the computation of the anomalous electric field within the target itself this leads to a matrix problem with a dense coefficient matrix it is well known that in general the presence of many grid cells creates a computational disadvantage for dense matrix methods compared to sparse matrix methods the sie approach replaces the dense matrix part of rigorous ie modeling by sparse matrix calculations based on an approximation of maxwell s equations the approximation is justified theoretically if a certain dimensionless parameter is small as opposed to approximations of the born type the validity of the sie approach does not rely on the anomalous field to be small in comparison with the background field in the target region

global solutions for the gravity water waves system in 2d we consider the gravity water waves system in the case of a one dimensional interface for sufficiently smooth and localized initial data and prove global existence of small solutions this improves the almost global existence result of wu invent math 177 1 45 135 2009 we also prove that the asymptotic behavior of solutions as time goes to infinity is different from linear unlike the three dimensional case germain et al ann math 175 2 691 754 2012 wu invent math 184 1 125 220 2011 in particular we identify a suitable nonlinear logarithmic correction and show modified scattering the solutions we construct in this paper appear to be the first global smooth nontrivial solutions of the gravity water waves system in 2d

almost global wellposedness of the 2 d full water wave problem we consider the problem of global in time existence and uniqueness of solutions of the 2 d infinite depth full water wave equation it is known that this equation has a solution for a time period 0 t e for initial data of the form e where t depends only on in this paper we show that for such data there exists a unique solution for a time period 0 e t e this is achieved by better understandings of the nature of the nonlinearity of the full water wave equation

large time existence for 3d water waves and asymptotics we rigorously justify in 3d the main asymptotic models used in coastal oceanography including shallow water equations boussinesq systems kadomtsev petviashvili kp approximation green naghdi equations serre approximation and full dispersion model we first introduce a variable nondimensionalized version of the water waves equations which vary from shallow to deep water and which involves four dimensionless parameters using a nonlocal energy adapted to the equations we can prove a well posedness theorem uniformly with respect to all the parameters its validity ranges therefore from shallow to deep water from small to large surface and bottom variations and from fully to weakly transverse waves

exponential stabilization of memristive neural networks with time delays in this paper a general class of memristive neural networks with time delays is formulated and studied some sufficient conditions in terms of linear matrix inequalities are obtained in order to achieve exponential stabilization the result can be applied to the closed loop control of memristive systems in particular several succinct criteria are given to ascertain the exponential stabilization of memristive cellular neural networks in addition a simplified and effective algorithm is considered for design of the optimal controller these conditions are the improvement and extension of the existing results in the literature two numerical examples are given to illustrate the theoretical results via computer simulations

stability and l_ 2 performance analysis of stochastic delayed neural networks this brief focuses on the robust mean square exponential stability and l2 performance analysis for a class of uncertain time delay neural networks perturbed by both additive and multiplicative stochastic noises new mean square exponential stability and l2 performance criteria are developed based on the delay partition lyapunov krasovskii functional method and generalized finsler lemma which is applicable to stochastic systems the analytical results are established without involving any model transformation estimation for cross terms additional free weighting matrices or tuning parameters numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones

splash singularities for a general oldroyd model with finite weissenberg number in this paper we study a 2d free boundary oldroyd b model which describes the evolution of a viscoelastic fluid we prove the existence of splash singularities namely points where the free boundary remains smooth but self intersects this paper extends the previous results obtained for the infinite weissenberg number by the authors in di iorio et al splash singularity for a free boundary incompressible viscoelastic fluid model 2018 arxiv 1806 11089 splash singularity for a 2d oldroyd b model with nonlinear piola kirchhoff stress nonlinear differ equ appl 24 60 2017 to the more realistic physical case of any finite weissenberg number the main difficulty faced in this paper is due to the non linear balance law of the elastic tensor which cannot be reduced as in the case of infinite weissenberg to a transport equation for the deformation gradient overcoming this difficulty requires a very accurate local existence theorem in terms of dependence on the weissenberg number the method in this case is based on the combined use of conformal transformations and lagrangian coordinates whose formulation must however take into account the general balance law of the elastic tensor and its dependence on the weissenberg number the existence of the splash singularities is therefore guaranteed by an adequate choice of initial data depending also on the elastic tensor combined with stability estimates

well posedness in sobolev spaces of the full water wave problem in 2 d we consider the motion of the interface of 2 d irrotational incompressible inviscid water wave with air above water and surface tension zero we show that the interface is always not accelerating into the water region normal to itself as rapidly as the normal acceleration of gravity as long as the interface is nonself intersect we therefore obtain the existence and uniqueness of solutions of the full water wave problem locally in time for any initial interface which is nonself intersect including the case that the interface is of multiple heights

well posedness of the water waves equations 1 1 presentation of the problem the water waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect incompressible irrotational fluid under the influence of gravity in this paper we restrict our attention to the case when the surface is a graph parameterized by a function x where t denotes the time variable and x xi xd rd the horizontal spatial variables the method developed here works equally well for any integer d 1 but the only physically relevant cases are of course d 1 and d 2 the layer of fluid is also delimited from below by a not necessarily flat bottom parameterized by a time independent function b x we denote by q t the fluid domain at time t the incompressibility of the fluids is expressed by 1 1 div v 0 in qu t 0

well posedness of the free surface incompressible euler equations with or without surface tension we provide a new method for treating free boundary problems in perfect fluids and prove local in time well posedness in sobolev spaces for the free surface incompressible 3d euler equations with or without surface tension for arbitrary initial data and without any irrotationality assumption on the fluid this is a free boundary problem for the motion of an incompressible perfect liquid in vacuum wherein the motion of the fluid interacts with the motion of the free surface at highest order

state estimation for delayed genetic regulatory networks with reaction diffusion terms this paper addresses the problem of state estimation for delayed genetic regulatory networks dgrns with reaction diffusion terms using dirichlet boundary conditions the nonlinear regulation function of dgrns is assumed to exhibit the hill form the aim of this paper is to design a state observer to estimate the concentrations of mrnas and proteins via available measurement techniques by introducing novel integral terms into the lyapunov krasovskii functional and by employing the wirtinger type integral inequality the convex approach green s identity the reciprocally convex approach and wirtinger s inequality an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities lmis the stability criterion depends upon the bounds of delays and their derivatives it should be noted that if the set of lmis is feasible then the desired observation of dgrns is possible and the state estimation can be determined finally two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design

splash singularity for a free boundary incompressible viscoelastic fluid model abstract in this paper we analyze a 2d free boundary viscoelastic fluid model of oldroyd b type at infinite weissenberg number our main goal is to show the existence of the so called splash singularities namely points where the boundary remains smooth but self intersects the combination of existence and stability results allows us to construct a special class of initial data which evolve in time into self intersecting configurations to this purpose we apply the classical conformal mapping method and later we move to the lagrangian framework as a consequence we deduce the existence of splash singularities this result extends the result obtained for the navier stokes equations in 4

on the free boundary problem of three dimensional incompressible euler equations in this paper we consider in three dimensions the motion of a general inviscid incompressible fluid with a free interface that separates the fluid region from the vacuum we assume that the fluid region is below the vacuum and that there is no surface tension on the free surface then we prove the local well posedness of the free boundary problem in sobolev space provided that there is no self intersection point on the initial surface and under the stability assumption that with being restricted to the initial surface 2007 wiley periodicals inc

well posedness in sobolev spaces of the full water wave problem in 3 d we consider the motion of the interface separating an inviscid incompressible irrotational fluid from a region of zero density in three dimensional space we assume that the fluid region is below the vacuum the fluid is under the influence of gravity and the surface tension is zero assume that the density of mass of the fluid is one the gravitational field is 0 0 1 the free interface is t at time t 0 and the fluid occupies the region t the motion of the fluid is described by vt v v 0 0 1 p on t t 0 euler s equation 1 1 div v 0 on t t 0 incompressible 1 2 curl v 0 on t t 0 irrotational 1 3 where v v1 v2 v3 is the fluid velocity p is the fluid pressure since we neglect the surface tension the pressure is zero on the interface so on the interface p 0 on t 1 4 1 v is tangent to the free surface t t 1 5 we want to find solutions of system 1 1 1 5 taking prescribed initial data such that for every fixed t 0 t approaches the xy plane at infinity and v x y z t 0 vt x y z t 0 as x y z since the fluid is assumed irrotational incompressible we can reduce the study of the entire motion to the motion of the free surface the above model is a 3 d water wave model it is generally known that when surface tension is neglected the motion of the interface between an inviscid fluid and vacuum under the influence of gravity can be subject to taylor instability 8 22 in a previous work 24 we studied the 2 dimensional water wave model we showed that for a 2 d water wave the sign condition relating to taylor instability always holds for nonself intersecting interface that is the motion of the interface is not subject to taylor instability we showed further that the 2 d full nonlinear water wave problem is uniquely solvable in sobolev spaces locally in time for any initially nonself intersecting interface earlier works on the well posedness in sobolev spaces of the 2 d water wave problem include nalimov 18 yosihara 25 and walter craig 6 where the main results concern the well posedness of the

geometry and a priori estimates for free boundary problems of the euler s equation in this paper we derive estimates to the free boundary problem for the euler equation with surface tension and without surface tension provided the rayleigh taylor sign condition holds we prove that as the surface tension tends to 0 when the rayleigh taylor condition is satisfied solutions converge to the euler flow with zero surface tension 2007 wiley periodicals inc

well posedness for the classical stefan problem and the zero surface tension limit we develop a framework for a unified treatment of well posedness for the stefan problem with or without surface tension in the absence of surface tension we establish well posedness in sobolev spaces for the classical stefan problem we introduce a new velocity variable which extends the velocity of the moving free boundary into the interior domain the equation satisfied by this velocity is used for the analysis in place of the heat equation satisfied by the temperature solutions to the classical stefan problem are then constructed as the limit of solutions to a carefully chosen sequence of approximations to the velocity equation in which the moving free boundary is regularized and the boundary condition is modified in a such a way as to preserve the basic nonlinear structure of the original problem with our methodology we simultaneously find the required stability condition for well posedness and obtain new estimates for the regularity of the moving free boundary finally we prove that solutions of the stefan problem with positive surface tension sigma converge to solutions of the classical stefan problem as sigma to 0

multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions multistability is a property necessary in neural networks in order to enable certain applications e g decision making where monostable networks can be computationally restrictive this article focuses on the analysis of multistability for a class of recurrent neural networks with unsaturating piecewise linear transfer functions it deals fully with the three basic properties of a multistable network boundedness global attractivity and complete convergence this article makes the following contributions conditions based on local inhibition are derived that guarantee boundedness of some multistable networks conditions are established for global attractivity bounds on global attractive sets are obtained complete convergence conditions for the network are developed using novel energy like functions and simulation examples are employed to illustrate the theory thus developed

nontrivial global attractors in 2 d multistable attractor neural networks attractor dynamics is a crucial problem for attractor neural networks as it is the underling computational mechanism for memory storage and retrieval in neural systems this brief studies a class of attractor network consisting of linearized threshold neurons and analyzes global attractors based on a parameterized 2 d model on the basis of previous results on nondegenerate and degenerate equilibria in mathematics we further elucidate all possible nontrivial global attractors our theoretical result provides precise descriptions on how the changes of network parameters affect the attractors distribution and landscape and it may give a feasible solution towards specifying attractors by specifying weights simulations are presented to illustrate the theoretical results