global existence and nonexistence of solution for cauchy problem of multidimensional double dispersion equations abstract in this paper we consider the cauchy problem of multidimensional generalized double dispersion equations u t t u u t t 2 u f u where f u a u p by potential well method we prove the existence and nonexistence of global weak solution without establishing the local existence theory and we derive some sharp conditions for global existence and lack of global existence solution

on the wave equation with hyperbolic dynamical boundary conditions interior and boundary damping and supercritical sources abstract the aim of this paper is to study the problem u t t u p x u t f x u in 0 u 0 on 0 0 u t t u u q x u t g x u on 0 1 u 0 x u 0 x u t 0 x u 1 x in where is a bounded open subset of r n with c 1 boundary n 2 1 is relatively open on denotes the laplace beltrami operator on is the outward normal to and the terms p and q represent nonlinear damping terms while f and g are nonlinear perturbations in the paper we establish local and global existence uniqueness and hadamard well posedness results when source terms can be supercritical or super supercritical

instability of standing waves for klein gordon zakharov equations with different propagation speeds in three space dimensions abstract this paper is concerned with the standing wave for klein gordon zakharov equations with different propagation speeds in three space dimensions the existence of standing wave with the ground state is established by applying an intricate variational argument and the instability of the standing wave is shown by applying pagne and sattinger s potential well argument and levine s concavity method

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

explicitly stable fundamental measure theory models for classical density functional theory the derivation of the state of the art tensorial versions of fundamental measure theory a form of classical density functional theory for hard spheres is reexamined in the light of the recently introduced concept of global stability of the density functional based on its boundedness lutsko and lam phys rev e 98 012604 2018 2470 004510 1103 physreve 98 012604 it is shown that within the present paradigm explicit stability of the functional can be achieved only at the cost of giving up accuracy at low densities it is argued that this is an acceptable trade off since the main value of dft lies in the study of dense systems explicit calculations for a wide variety of systems show that a proposed explicitly stable functional is competitive in all ways with the popular white bear models while sharing some of their weaknesses when applied to non close packed solids

the initial boundary value problems for a class of nonlinear wave equations with damping term abstract in this paper we study the existence and uniqueness of the global generalized solution and the global classical solution the blowup of the solution and the energy decay of the solutions of the initial boundary value problems for a class of nonlinear wave equations

the nonuniform hard rod fluid revisited the statistical mechanics of the one dimensional nonuniform pure hard core fluid is formulated in the spirit of the reiss frisch lebowitz rfl scaled particle theory by emphasizing the importance of the core dependence a more intuitive and simpler derivation can be given the wiener hopf type construction of the pair direct correlation function is formulated via the dyson variational method of inverse scattering theory which is compared with the particle hole theory the new approach allows us to lift the global free energy functional into a larger space where all the symmetries become apparent

the inverse problem in classical statistical mechanics we address the problem of whether there exists an external potential corresponding to a given equilibrium single particle density of a classical system results are established for both the canonical and grand canonical distributions it is shown that for essentially all systems without hard core interactions there is a unique external potential which produces any given density the external potential is shown to be a continuous function of the density and in certain cases it is shown to be differentiable as a consequence of the differentiability of the inverse map which is established without reference to the hard core structure in the grand canonical ensemble we prove the existence of the ornstein zernike direct correlation function a set of necessary but not sufficient conditions for the solution of the inverse problem in systems with hard core interactions is derived

blow up and critical exponents for nonlinear hyperbolic equations we prove nonexistence results for the cauchy problem for the abstract hyperbolic equation in a banach space x utt f u t 0 u 0 u0 ut 0 u1 where f x r is a c1 function several applications to the second and higher order hyperbolic equations with local and nonlocal nonlinearities are presented we also describe an approach to kato s and john s critical exponents for the semilinear equations ut u b x t u p p 1 which are responsible for phenomena of stability unstability blow up and asymptotic behaviour

stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions abstract sufficient conditions for the local exponential stabilizability of abstract systems described by an arbitrary co semigroup with nonlinear unbounded perturbations are formulated applications to parabolic and in particular hyperbolic problems with nonlinearity appearing in the boundary conditions are given

fundamental measure density functional theory for nonadditive hard core mixtures the one dimensional case we treat a one dimensional binary mixture of hard core particles that possess nonadditive diameters for this model a density functional theory is constructed following similar principles as an earlier extension of rosenfeld s fundamental measure theory to three dimensional nonadditive hard sphere mixtures the theory applies to arbitrary positive and moderate negative nonadditivity and reduces to percus exact functional in the additive case bulk direct correlation functions are obtained as functional derivatives of the excess free energy functional results for the partial pair correlation functions in bulk as calculated via the ornstein zernike route and using the direct correlation functions as input show very good agreement with results from our monte carlo computer simulations of the mixture

control and synchronization of neuron ensembles synchronization of oscillations is a phenomenon prevalent in natural social and engineering systems controlling synchronization of oscillating systems is motivated by a wide range of applications from surgical treatment of neurological diseases to the design of neurocomputers in this paper we study the control of an ensemble of uncoupled neuron oscillators described by phase models we examine controllability of such a neuron ensemble for various phase models and furthermore study the related optimal control problems in particular by employing pontryagin s maximum principle we analytically derive optimal controls for spiking single and two neuron systems and analyze the applicability of the latter to an ensemble system finally we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations the methodology developed here is universal to the control of general nonlinear phase oscillators

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

type i membranes phase resetting curves and synchrony type i membrane oscillators such as the connor model connor et al 1977 and the morris lecar model morris and lecar 1981 admit very low frequency oscillations near the critical applied current hansel et al 1995 have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive we use singular perturbation methods and averaging to show that this is a general property of type i membrane models we show in a limited sense that so called type ii resetting occurs with models that obtain rhythmicity via a hopf bifurcation we also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions

long time behavior of a class of thermoelastic plates with nonlinear strain abstract in recent years a class of vibrating plates with nonlinear strain of p laplacian type was studied by several authors the present paper contains a first thermoelastic model of that class of problems including both fourier and non fourier heat laws our main result establishes the existence of global and exponential attractors for the strongly damped problem through a stabilizability inequality in addition for the weakly damped problem we establish the exponential stability of its galerkin semiflows

blow up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities abstract we investigate a hyperbolic pde modeling wave propagation in viscoelastic media under the influence of a linear memory term of boltzmann type and a nonlinear damping modeling friction as well as an energy amplifying supercritical nonlinear source u t t k 0 u 0 k s u t s d s u t m 1 u t u p 1 u in 0 t u x t u 0 x t in 0 where is a bounded domain in r 3 with a dirichlet boundary condition the relaxation kernel k is monotone decreasing and k 1 we study blow up of solutions when the source is stronger than dissipations i e p max m k 0 under two different scenarios first the total energy is negative and the second the total energy is positive with sufficiently large quadratic energy this manuscript is a follow up work of the paper 30 in which hadamard well posedness of this equation has been established in the finite energy space the model under consideration features a supercritical source and a linear memory that accounts for the full past history as time goes to which is distinct from other relevant models studied in the literature which usually involve subcritical sources and a finite time memory

deriving the rosenfeld functional from the virial expansion in this article we replace the semiheuristic derivation of the rosenfeld functional of hard convex particles with the systematic calculation of mayer clusters it is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number this extends the virial expansion of the free energy by an expansion in the loop order with the rosenfeld functional as its leading contribution rosenfeld s weight functions then follow from the derivation of the intersection probability by generalizing the equation of blaschke santalo and chern it is found that the 0 loop order can be derived exactly and reproduces the rosenfeld functional we further discuss the influence of particle dimensions topologies and geometries on the mathematical structure of the calculation

dynamics around the ground state of a nonlinear evolution equation we analyze the qualitative behavior of solutions forwards and backwards we present characterizations of blowup boundedness and convergence to the ground state as t we define and use a potential well and several invariant and positive invariant sets 2005 elsevier ltd all rights reserved

stabilization of wave and plate like equations with nonlinear dissipation on the boundary abstract in this paper we consider second order in time equations of petrovsky type wave and plate like with nonlinear dissipative boundary conditions under certain geometric conditions imposed on the domain the results on asymptotic behavior of the solutions are established

density functional theory for nearest neighbor exclusion lattice gases in two and three dimensions to speak about fundamental measure theory obliges us to mention dimensional crossover this feature inherent to the systems themselves was incorporated in the theory almost from the beginning although at first it was thought to be a consistency check for the theory it rapidly became its fundamental pillar thus becoming the only density functional theory which possesses such a property it is straightforward that dimensional crossover connects for instance the parallel hard cube system three dimensional with that of squares two dimensional and rods one dimensional we show here that there are many more connections which can be established in this way through them we deduce from the functional for parallel hard hyper cubes in the simple hyper cubic lattice the corresponding functionals for the nearest neighbor exclusion lattice gases in the square triangular simple cubic face centered cubic and body centered cubic lattices as an application the bulk phase diagram for all these systems is obtained

phase resetting of collective rhythm in ensembles of oscillators phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations we consider globally coupled ensembles of sakaguchi kuramoto oscillators and use the ott antonsen theory of ensemble evolution to derive the analytical phase resetting equations we show the final phase reset value to be composed of two parts an immediate phase reset directly caused by the perturbation and the dynamical phase reset resulting from the relaxation of the perturbed system back to its dynamical equilibrium analytical semianalytical and numerical approximations of the final phase resetting curve are constructed we support our findings with extensive numerical evidence involving identical and nonidentical oscillators the validity of our theory is discussed in the context of large ensembles approximating the thermodynamic limit

density functional theory for fluids in porous media as models for substances adsorbed within amorphous solid matrices we consider mixtures of spheres with either hard or ideal interactions where several matrix components are quenched and the remaining adsorbate components are equilibrated we propose a density functional theory based on the exact zero dimensional limit which treats both matrix and adsorbate components on the level of the respective one body density profiles as a test we calculate pair correlation functions for hard spheres adsorbed in either a hard sphere or an ideal sphere matrix and find good agreement with our computer simulation results

deriving fundamental measure theory from the virial series consistency with the zero dimensional limit fundamental measure theory fmt for hard particles has great potential for predicting the phase behavior of colloidal and nanometric shapes the modern versions of fmt are usually derived from the zero dimensional limit a system of at most one particle confined in a collection of cavities in the limit that all cavities shrink to the size of the particle in phys rev e 85 041150 2012 a derivation from an approximated and resummed virial expansion was presented whose result was not fully consistent with the fmt from the zero dimensional limit here we improve on this derivation and obtain exactly the same fmt functional as was obtained earlier from the zero dimensional limit as a result further improvements of fmt based on the virial expansion can now be formulated some of which we suggest in the outlook

critical and sup critical initial energy finite time blowup phenomena for the fourth order wave equations with nonlinear strain term abstract this paper is devoted to the blowup phenomena for a class of fourth order wave equation with nonlinear strain term first for the model equation with strain structure we prove the finite time blowup of solution for the critical initial energy i e e 0 d then the finite time blowup and the upper bound of the blowup time are established for the sup critical initial energy i e e 0 0

dimensional crossover of the fundamental measure functional for parallel hard cubes we present a regularization of the recently proposed fundamental measure functional for a mixture of parallel hard cubes the regularized functional is shown to have correct dimensional crossovers to any smaller dimension thus allowing its use to study highly inhomogeneous phases such as the solid phase furthermore it is shown how the functional of the slightly more general model of parallel hard parallelepipeds can be obtained using the zero dimensional functional as a generating functional extensions to the multicomponent system a restricted orientation model and mixtures or prallel hard cylinders are also given s0031 9007 97 03105 0

a weakly nonlinear analysis of elasto plastic microstructure models at certain critical values of the hardening modulus the governing equations of elasto plastic flow may lose their hyperbolicity and exhibit two modes of ill posedness shear band and flutter ill posedness these modes of ill posedness are characterized by the uncontrolled growth of modes at infinitely fine scales which ultimately violates the continuum assumption in previous work l an and a peirce siam j appl math 54 1994 pp 708 730 a continuum model accounting for microscale deformations was built linear analysis demonstrated the regularizing effect of the microstructure and provided a relationship between the width of the localized instabilities and the microlength scale in this paper a weakly nonlinear analysis is used to explore the immediate post critical behavior of the solutions for both one dimensional and anti plane shear models post critical deformations in the plastic regions are shown to be governed by the boussinesq equation one of the completely integrable pdes having so

a characterization of global and nonglobal solutions of nonlinear wave and kirchhoff equations we give necessary and sufficient conditions for existence of global and nonglobal solutions of a nonlinear wave equation in a bounded domain we consider nonlinear dissipation and a nonlinear source term we also analyze the qualitative behavior of solutions forwards and backwards for the wave equation without dissipation in this case we present characterizations of blow up and asymptotic behavior finally we extend some of our results to a nonlinear kirchhoff equation we use the concepts of stable and unstable sets introduced by payne and sattinger in 1975

on existence and asymptotic stability of solutions of the degenerate wave equation with nonlinear boundary conditions abstract we study the global existence of solutions of the nonlinear degenerate wave equation 0 x y y 0 in 0 y 0 on 1 0 y y f y g y 0 on 0 0 y x 0 y 0 y x 0 y 1 x in where y denotes the derivative of y with respect to parameter t f s c0 s s and g is a nondecreasing c1 function such that k1 s 2 g s s k2 s 2 for some k1 k2 0 with 0 0 if n 1 2 the existence of solutions is proved by means of the faedo galerkin method furthermore when 0 the uniform decay is obtained by making use of the perturbed energy method

constrained charge balanced minimum power controls for spiking neuron oscillators abstract in this paper we study the optimal control of phase models for spiking neuron oscillators we focus on the design of minimum power current stimuli that elicit spikes of neurons at specified times subject to the charge balance constraint such charge balanced controls in practice are used to suppress undesirable side effects occurred due to the accumulation of electric charge resulting from the applied external stimuli we derive charge balanced minimum power controls for a general phase model using the maximum principle where the cases with unbounded and bounded control amplitude are examined the latter is of fundamental importance because phase models are valid under weak forcing the developed optimal control strategies are applied to both mathematically ideal and experimentally observed phase models to demonstrate their applicability including the widely studied hodgkin huxley model

cluster density functional theory for lattice models based on the theory of mobius functions rosenfeld s fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of mobius functions of partially ordered sets the free energy density functional is expressed as an expansion in a finite set of lattice clusters this set is endowed with a partial order so that the coefficients of the cluster expansion are connected to its mobius function because of this it is rigorously proven that a unique such expansion exists for any lattice model the low density analysis of the free energy functional motivates a redefinition of the basic clusters zero dimensional cavities which guarantees a correct zero density limit of the pair and triplet direct correlation functions this new definition extends rosenfeld s theory to lattice models with any kind of short range interaction repulsive or attractive hard or soft one or multicomponent finally a proof is given that these functionals have a consistent dimensional reduction i e the functional for dimension d can be obtained from that for dimension d d d if the latter is evaluated at a density profile confined to a d dimensional subset

exact density functionals in one dimension we propose a new and general method for deriving exact density functionals in one dimension for lattice gases with finite range pairwise interactions corresponding continuum functionals are derived by applying a proper limiting procedure the method is based on a generalized markov property which allows us to set up a rather transparent scheme that covers all previously known exact functionals for one dimensional lattice gas or fluid systems implications for a systematic construction of approximate density functionals in higher dimensions are pointed out

two hard spheres in a spherical pore exact analytic results in two and three dimensions the partition function and the one and two body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore the equivalent problem for hard disks is addressed too we establish a relation valid for any dimension between these partition functions second virial coefficient for inhomogeneous systems in a spherical pore and third virial coefficients for polydisperse hard spheres mixtures using the established relation we were able to evaluate the cluster integral b2 v related with the second virial coefficient for the hard disc system into a circular pore finally we analyse the behaviour of the obtained expressions near the maximum density

the dynamics of a nonlinear wave equation we consider a wave equation in a bounded domain with linear dissipation and with a nonlinear source term we give characterizations of all the solutions with respect to their qualitative properties globality boundedness nonglobality blow up and convergence to equilibria

invariance and existence analysis for semilinear hyperbolic equations with damping and conical singularity abstract in this paper we will discuss about the invariance of solution set and present the existence and non existence of the global solutions a class of initial boundary value problems with dissipative terms is considered for a class of semilinear degenerate hyperbolic equations on the cone sobolev spaces first we will discuss the invariance of some sets corresponding to the problem 1 1 and then by using a family of potential wells and concavity methods we obtain existence and non existence results of global solutions with exponential decay and show the blow up in finite time of solutions on a manifold with conical singularities

existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term the wave equation with a source term is considered utt u u uin 0 we prove the existence and uniform decay rates of the energy by assuming a nonlinear feedback ut acting on the boundary provided that has necessarily not a polynomial growth near the origin to obtain the existence of global solutions we make use of the potential well method combined with the faedo galerkin procedure and constructing a special basis furthermore we prove that the energy of the system decays uniformly to zero and we obtain an explicit decay rate estimate adapting the ideas of lasiecka and tataru differential integral equations 6 3 1993 507 and patrick martinez esain control optimisation calc var 4 1999 419 the resulting problem generalizes martinez results and complements the works of lasiecka and tataru 1993 and vitillaro glasgow math j 44 2002 375

on potential wells and vacuum isolating of solutions for semilinear wave equations abstract in this paper we study the initial boundary value problem of semilinear wave equations u tt u u p 1 u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 where r n is a bounded domain 1 1 n 2 n 2 for n 3 first by using a new method we introduce a family of potential wells which include the known potential well as a special case then by using it we obtain some new existence theorems of global solutions and prove that for any e 0 d d is the depth of the known potential well all solutions with initial energy e 0 satisfying 0 h 0 1

on the initial boundary problem for fourth order wave equations with damping strain and source terms abstract in this paper we study the global existence and blow up of solutions to the fourth order equations u t t u t 2 u u i 1 n x i i u x i f u x t 0 where 0 under appropriate assumptions on the initial data and parameters in the above equation we establish two results on blow up of solutions with arbitrary initial energy e 0 also by using a potential well we show the global existence of solutions for the fourth order wave equation with some i s and f s especially it is proved that the energy decays exponentially as t

decay of energy for second order boundary hemivariational inequalities with coercive damping abstract in this article we consider the asymptotic behavior of solutions to second order evolution inclusions with the boundary multivalued term u t a t u t b u t j t u t 0 and u t a t u t b u t j t u t 0 where a is a possibly nonlinear coercive and pseudomonotone operator b is linear continuous symmetric and coercive is the trace operator and j is a locally lipschitz integral functional with denoting the clarke generalized gradient taken with respect to the second variable for both cases we provide conditions under which the appropriately defined energy decays exponentially to zero as time tends to infinity we discuss assumptions and provide examples of multivalued laws that satisfy them

density functional for the widom rowlinson model we present a density functional theory for the m component widom rowlinson model for a mixture of spherical particles where the unlike species interact with a hard core potential and the interactions between like species vanish the functional is exact for small densities and in the zero dimensional limit it predicts the fluid structure in good agreement with simulations and yields a continuous demixing phase transition for m 2 in the limit of large m the widom rowlinson model reduces to effective hard spheres in the mixed phase and the asakura oosawa colloid ideal polymer model in the demixed phase within the present theory both cases are captured correctly for intermediate m we find a first order demixing phase transition with a rapidly broadening density discontinuity upon increasing m

global existence and blow up of solutions for some hyperbolic systems with damping and source terms abstract this paper deals with the global existence and blow up of solutions to some nonlinear hyperbolic systems with damping and source terms in a bounded domain by using the potential well method we obtain the global existence moreover for the problem with linear damping terms blow up of solutions is considered and some estimates for the lifespan of solutions are given

on the validity of the inverse conjecture in classical density functional theory it is shown that the basic assumptions of the classical density functional approach are rigorously correct forh stable systems in the grand canonical ensemble moreover it is established that the set of all single particle densities is convex these results are derived by providing necessary and sufficient conditions for the solution of the classical inverse problem for single particle densities analogous results are obtained for the solution of the higher order correlation inverse problem and the ramifications of these results for the validity of two body decomposition of forces are discussed

global nonexistence for a semilinear wave equation with nonlinear boundary dissipation in this paper we consider the following problem ytt yxx yt y p 1y x t 0 l 0 t y 0 t 0 t 0 t yx l t y l t yt l t m 1yt l t 0 t 0 t y x 0 y0 x yt x 0 y1 x x 0 l where 0 l is a bounded open interval in r p 1 and m 1 we are interested in the interaction between the boundary damping yt l t m 1yt l t and the interior source y t p 1y t under some appropriate assumptions on the initial data two blow up results with positive initial energy are established furthermore we obtain that the solutions blow up if p or y0 l is sufficiently large

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

nonlinear parabolic equations with critical initial conditions j u0 d or i u0 0 abstract in this paper we study the initial boundary value problem of nonlinear parabolic equation u t i 1 n x i u x i p 2 u x i u 1 x t 0 u x 0 u 0 x x u x t 0 x t 0 where r n is a bounded domain p p n p np n p if p n by using potential well method we prove that if 0 u 0 x w 0 1 p j u 0 d i u 0 0 or i u 0 0 0 j u 0 d then the problem admits a global solution u t l 0 w 0 1 p with u t t l 2 0 l 2 and u t w for 0 t

design of charge balanced time optimal stimuli for spiking neuron oscillators in this letter we investigate the fundamental limits on how the interspike time of a neuron oscillator can be perturbed by the application of a bounded external control input a current stimulus with zero net electric charge accumulation we use phase models to study the dynamics of neurons and derive charge balanced controls that achieve the minimum and maximum interspike times for a given bound on the control amplitude our derivation is valid for any arbitrary shape of the phase response curve and for any value of the given control amplitude bound in addition we characterize the change in the structures of the charge balanced time optimal controls with the allowable control amplitude we demonstrate the applicability of the derived optimal control laws by applying them to mathematically ideal and experimentally observed neuron phase models including the widely studied hodgkin huxley phase model and by verifying them with the corresponding original full state space models this work addresses a fundamental problem in the field of neural control and provides a theoretical investigation to the optimal control of oscillatory systems

the classical fluid of associating hard rods in an external field two models of one dimensional fluids of associating hard rods in an arbitrary external field are investigated in the first model particles can only form dimers while in the second model which has been solved previously by percus aggregates of any size coexist in both cases the grand canonical potential and the external potential are found exactly as functionals of the density it is shown that wertheim s thermodynamic perturbation theory of polymerization provides a straightforward route to the exact solution by expanding the functional space to include more density parameters this suggests that wertheim s theory should be used also for studying the structure and not only the thermo dynamics of real associating fluids

multidimensional viscoelasticity equations with nonlinear damping and source terms abstract in this paper we study the initial boundary value problem of multidimensional viscoelasticity equations u tt u t i 1 n x i i u x i f u t g u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 where r n is a bounded domain i s1 i s2 s1 s2 0 f s s 0 g s s 0 and satisfy some growth conditions first we introduce a family of potential wells by using a new method then using it we obtain some new existence theorems of global solutions and behaviour of vacuum isolation of solutions

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

density functional theory for soft interactions by dimensional crossover a density functional theory for spherical particles interacting via an arbitrary soft pair potential is presented the derivation is solely based on limits where the behavior is exactly known namely a zero dimensional cavity and the low density virial expansion the approach generalizes the fundamental measure theory for hard bodies and yields the structure and thermodynamics of the homogeneous fluid as an output we apply the theory to an ultrasoft logarithmic potential that mimics star polymers in a good solvent the theory when supplemented by a rescaling procedure reproduces the peculiar features of the pair correlations in this system that we also find in computer simulations

fundamental measure theory and dimensional interpolation for the hard spheres fluid abstract this paper presents a short review of the recent advances in the development of density functional for hard spheres the fundamental measure theory as developed originally by y rosenfeld and in its more recent versions is compared with other density functional approximations the results for dimensional crossover from the hard spheres fluid in three dimensions to hard rods in one dimension and to zero dimensional cavities are discussed new results on the fluid crystal coexistence and on the crossover to the hard disc fluid in two dimensions are presented

on nonlinear wave equations with degenerate damping and source terms in this article we focus on the global well posedness of the differential equation u tt u u k j u t u p 1 u in x 0 t where j is a sub differential of a continuous convex function j under some conditions on j and the parameters in the equations we obtain several results on the existence of global solutions uniqueness nonexistence and propagation of regularity under nominal assumptions on the parameters we establish the existence of global generalized solutions with further restrictions on the parameters we prove the existence and uniqueness of a global weak solution in addition we obtain a result on the nonexistence of global weak solutions to the equation whenever the exponent p is greater than the critical value k m and the initial energy is negative we also address the issue of propagation of regularity specifically under some restriction on the parameters we prove that solutions that correspond to any regular initial data such that u 0 h 2 h 1 0 u 1 h 1 0 are indeed strong solutions

on the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids it is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density we derive the explicit form that the functional takes for a system of hard rods and propose an approximate one for hard spheres attractive interactions are also considered in mean field approximation in all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated

from zero dimension cavities to free energy functionals for hard disks and hard spheres we present a systematic approach to derive fundamental measure theory free energy functionals for hard disks and hard spheres entirely from the exact free energy in the zero dimensional limit of a narrow cavity which cannot hold more than one molecule the functionals are within the generic class that includes the previous successful versions but have the remarkable property to yield the exact functional for quasi one dimensional density distributions

on potential wells to a semilinear hyperbolic equation with damping and conical singularity abstract this article deals with a semilinear hyperbolic equation with damping and conical singularity that was built by alimohammady et al 2017 1 where the weak solution with low initial energy i 0 d d is the potential well depth was considered we extend the previous results in the following three aspects firstly we consider the vacuum isolating behavior of the solution for initial energy i 0 0 and 0 i 0 d respectively we find that there are two explicit vacuum regions an annulus and a ball moreover we obtain the asymptotic behavior of the energy functional as t tends to the maximal existence time and then two necessary and sufficient conditions for the weak solution existing globally and blowing up in finite time are obtained secondly we discuss the weak solution with critical initial energy and establish the global existence and nonexistence results finally the weak solution with arbitrary positive initial energy is studied in this case the initial conditions such that the weak solution exists globally and blows up in finite time are given

finite size analysis of the hard square lattice gas we investigate the hard square lattice gas model by means of transfer matrix calculations and a finite size scaling analysis using a minimal set of assumptions we find that the spectrum of correction to scaling exponents is consistent with that of the exactly solved ising model and that the critical exponents and correlation length amplitudes closely follow the relation predicted by conformal invariance assuming that these spectra are exactly identical and conformal invariance we determine the critical point the conformal anomaly and the temperature and magnetic exponents with numerical margins of 10 11 or less these results are in a perfect agreement with the exactly known ising universal parameters in two dimensions in order to obtain this degree of precision we included system sizes as large as feasible and used extended precision floating point arithmetic the latter resource provided a substantial improvement of the analysis despite the fact that it restricted the transfer matrix calculations to finite sizes of at most 34 lattice units

inhomogeneous ising model on the bethe lattice abstract a new approach to the spin 1 2 ising model with nonconstant interactions and a site dependent external field is presented it represents a straightforward way for solving the inverse problems the external field required to produce a given magnetization profile is given explicitly for spin 1 2 systems on the bethe lattice with an arbitrary coordination number q

the cauchy problem for the rosenau equation abstract this paper considers the existence and the uniqueness of the solution for the cauchy problem of the rosenau equation u t t u x 4 u x 4 t t u x x f u x x we prove the existence and the uniqueness of the global solution under some conditions of f u and give the condition for nonexistence of a global solution for f u u p u with 0 and p 0 the global existence and finite time blow up for the problem are proved with the aid of the potential well method

distribution functions for fluids in random media a random medium is considered composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure statistically homogeneous on all but molecular length scales the equilibrium statistical mechanics of a fluid contained inside this quenched medium is discussed various particle particle and particle obstacle correlation functions which differ from the corresponding functions for a fully equilibrated binary mixture are defined through an averaging process over the static ensemble of obstacle configurations and application of topological reduction techniques the ornstein zernike equations also differ from their equilibrium counterparts

global existence asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term abstract the paper studies the global existence asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term it proves that under rather mild conditions on nonlinear terms and initial data the above mentioned problem admits a global weak solution and the solution decays exponentially to zero as t respectively in the states of large initial data and small initial energy in particular in the case of space dimension n 1 the weak solution is regularized to be a unique generalized solution and if the conditions guaranteeing the global existence of weak solutions are not valid then under the opposite conditions the solutions of above mentioned problem blow up in finite time and an example is given

new collective modes of interaction nature in inhomogeneous ising networks we propose a vertex formulation of the ising model with inhomogeneous external field on multiconnected networks possessing a superbond structure the related technique based on gauge degrees of freedom enables us to recognize new collective modes of interaction nature which provide an exact solution of the inverse profile problem and an explicit form of a local free energy functional on an extended magnetization mode space application is made to a square strip

optimal design of minimum power stimuli for phase models of neuron oscillators in this paper we study optimal control problems of spiking neurons whose dynamics are described by a phase model we design minimum power current stimuli controls that lead to targeted spiking times in particular we consider bounded control amplitude and characterize the range of possible spiking times determined by the bound which can be chosen sufficiently small within the range where the phase model is valid we show that for a given bound the corresponding feasible spiking times are optimally achieved by piecewise continuous controls we present analytic expressions with numerical simulations of the minimum power stimuli for several phase models we demonstrate the applicability of our method with an experimentally determined phase response curve

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

global solutions and finite time blow up for fourth order nonlinear damped wave equation in this paper we study the initial boundary value problem and global well posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term which was introduced to describe the dynamics of a suspension bridge the global existence decay estimate and blow up of solution at both subcritical e 0 0 in this paper we study the initial boundary value problem and global well posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term which was introduced to describe the dynamics of a suspension bridge the global existence decay estimate and blow up of solution at both subcritical e 0 0

peel or coat spheres by convolution repeatedly a convolution transformation is presented that maps the four fundamental measures minkowski functionals of a three dimensional sphere to those of a sphere with a different radius it is shown that the set of all these transformations parametrized by the induced change in radius forms an abelian commutative group and hence constitutes a flexible framework for the manipulation of spheres the corresponding one dimensional case is laid out and the relationship to fundamental measure density functional theory is discussed briefly

entropy of a one dimensional mixed lattice gas this paper deals with the grand canonical entropy of a lattice gas mixture the entropy is a function of the multisite densities corresponding to the interaction pattern of the system in question it is first evaluated for a nearest neighborinteraction one dimensional simple lattice gas to show how the structure of bulk fluid is locally maintained generalization requires one set of interrelations among multisite densities presented in closed form for an arbitrary lattice and one set between boltzmann factors and multisite densities which is written down for simply connected lattices application is made to two row lattices which turn out to have local behavior from this viewpoint as do all single row or bethe lattices with complete range p interactions nonlocal examples are also given and suggestions made for approximation sequences in general lattices

global existence of solution for cauchy problem of multidimensional generalized double dispersion equations abstract we study the cauchy problem of a class of multidimensional generalized double dispersion equations u t t u u t t 2 u k u t f u we prove the global existence of weak solution under some assumptions on the nonlinear term and the initial data

asymptotic stability of the wave equation on compact manifolds and locally distributed damping a sharp result let m g be a n dimensional n geqq 2 compact riemannian manifold with boundary where g denotes a riemannian metric of class c this paper is concerned with the study of the wave equation on m g with locally distributed damping described by left begin array l u tt delta bf g u a x g u t 0 quad hbox on thinspace m times left 0 infty right u 0 hbox on partial m times left 0 infty right end array right where m represents the boundary of m and a x g ut is the damping term the main goal of the present manuscript is to generalize our previous result in cavalcanti et al trans ams 361 9 4561 4580 2009 treating the conjecture in a more general setting and extending the result for n dimensional compact riemannian manifolds m g with boundary in two ways i by reducing arbitrarily the region m ast subset m where the dissipative effect lies this gives us a totally sharp result with respect to the boundary measure and interior measure where the damping is effective ii by controlling the existence of subsets on the manifold that can be left without any dissipative mechanism namely a precise part of radially symmetric subsets an analogous result holds for compact riemannian manifolds without boundary

finite dimensional attractors for the kirchhoff models with critical exponents the paper studies the existence of the finite dimensional global attractor and exponential attractor for the dynamical system associated with the kirchhoff models utt u m 1 u ut 2u h ut g u f x it proves that for the subcritical and critical cases 1 m n 2 n 2 with n 6 the above mentioned dynamical system possesses in phase spaces x1 a finite dimensional global attractor and a weak exponential attractor respectively

a class of fourth order wave equations with dissipative and nonlinear strain terms we study the initial boundary value problem for a class of fourth order wave equations with dissipative and nonlinear strain terms by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolating of solutions but also give some threshold results of global existence and nonexistence of solutions

density functional theory for hard particles in n dimensions recently it has been shown that the heuristic rosenfeld functional can be derived from the virial expansion for particles overlapping in one center here we generalize this approach to any number of intersections starting from the virial expansion in ree hoover diagrams it is shown in the first part that each intersection pattern corresponds to exactly one infinite class of diagrams determining their automorphism groups we sum over all its elements and derive a generic functional the second part shows that this functional factorizes into a convolute of integral kernels for each intersection center we derive this kernel for n dimensional particles in the n dimensional flat euclidean space the third part focuses on three dimensions and determines the functionals for up to four intersection centers comparing the leading order to rosenfeld s result we close by proving a generalized form of the blaschke santalo chern equation of integral geometry

existence and asymptotic stability for evolution problems on manifolds with damping and source terms abstract one considers the nonlinear evolution equation with source and damping terms u tt au g u t u u on 0 where is a compact manifold we prove the global existence of solutions making use of the potential well method furthermore we study the asymptotic behaviour of solutions adapting the ideas introduced by patrick martinez in esaim control optim calc var 4 1999 419 444 when the frictional damping mechanism g on the manifold does not necessarily have a polynomial growth near the origin

generating function density functional theory free energy functionals and direct correlation functions for hard spheres abstract a recent density functional theory for the inhomogeneous hard sphere fluid expresses the free energy in terms of a set of derivatives with respect to the particle radius of a simple generating function in the present paper this generating function approach gfa is reformulated in terms of general conditions on the coefficients of the differential operator involved in the theory this gives more flexibility to the theory and allows for ready derivation of new functionals that are tested in the calculation of density profiles of hard spheres near a hard wall comparison with the results of the previous formulation of the gfa shows a better performance of the new functionals and also gives a much deeper understanding of the structure of the theory and its connections with the fundamental measures theory of rosenfeld a simple modification of the gfa pair direct correlation functions yields explicit analytic expressions with very good agreement with simulation results

general decay and blow up of solution for a quasilinear viscoelastic problem with nonlinear source abstract in this paper we consider a quasilinear viscoelastic wave equation in canonical form with the homogeneous dirichlet boundary condition we prove that for certain class of relaxation functions and certain initial data in the stable set the decay rate of the solution energy is similar to that of the relaxation function this result improves earlier ones obtained by messaoudi and tatar s a messaoudi n e tatar global existence and uniform stability of solutions for a quasilinear viscoelastic problem math methods appl sci 30 2007 665 680 in which only the exponential and polynomial decay rates are considered conversely for certain initial data in the unstable set there are solutions that blow up in finite time the last result is new since it allows a larger class of initial energy which may take positive values