asymptotic behavior of the solution to the non isothermal phase field equation we consider the penrose fife phase field model thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 with homogeneous neumann boundary condition to the nonlinear heat flux q 1 i e q 0 on the boundary where 0 is the temperature there is a unique h1 solution globally in time with the non empty connected compact limit set composed of stationary solutions and the linearized stable stationary solution is dynamically stable

a smoothing property of a hyperbolic system and boundary controllability abstract we investigate a method with which one can deduce controllability results from smoothing properties previous applications of the method were for partial differential equations like the euler bernoulli beam equation petrowski hyperbolic in this paper we study the method s applicability to a strictly hyperbolic system by considering the boundary controllability of a vibrating timoshenko beam with physical characteristics that may vary along the length of the beam two cases are considered a beam which is clamped at one end the other end being controlled by a torque and transverse force and a beam which is hinged at one end where a control torque is applied and free at the other end where a control force is applied

decay property for second order hyperbolic systems of viscoelastic materials we study a class of second order hyperbolic systems with dissipation which describes viscoelastic materials the considered dissipation is given by the sum of the memory term and the damping term when the dissipation is effective over the whole system we show that the solution decays in l 2 at the rate t n 4 as t provided that the corresponding initial data are in l 2 l 1 w heren is the space dimension the proof is based on the energy method in the fourier space also we discuss similar systems with weaker dissipation by introducing the operator 1 2 with 0 in front of the dissipation terms and

a non isothermal phase separation with constraints and dirichlet boundary condition for temperature abstract we consider non isothermal phase separation models of the penrose fife type which were proposed in o penrose p c fife thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 in the present paper we impose a non homogeneous dirichlet boundary condition on the nonlinear heat flux moreover we consider two cases as boundary conditions for the conserved order parameter one is the homogeneous neumann boundary condition and the other is the signorini boundary condition which is nonlinear we show the existence and uniqueness of solutions to these models

the timoshenko system with history and cattaneo law in this paper we study a fully hyperbolic thermoelastic timoshenko system with past history where the thermal effects are given by cattaneo s law we obtain exponential stability of solutions if and only if a new condition on the wave speed of propagation is verified otherwise when that condition fails we obtain polynomial stability of solutions in this case optimal rates of decay are established

energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria let h r be a c1 function on a real hilbert space h and let 0 be a positive damping parameter for any control function e r r which tends to zero as t we study the asymptotic behavior of the trajectories of the damped nonlinear oscillator hbfc x t x t x t e t x t 0 we show that if e t does not tend to zero too rapidly as t then the term e t x t asymptotically acts as a tikhonov regularization which forces the trajectories to converge to a particular equilibrium indeed in the main result of this paper it is established that when is convex and s argmin under the key assumption that e is a slow control i e 0 e t dt then each trajectory of the hbfc system strongly converges as t to the element of minimal norm of the closed convex set s as an application we consider the damped wave equation with neumann boundary condition formula

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

distance distribution in random graphs and application to network exploration we consider the problem of determining the proportion of edges that are discovered in an erdos renyi graph when one constructs all shortest paths from a given source node to all other nodes this problem is equivalent to the one of determining the proportion of edges connecting nodes that are at identical distance from the source node the evolution of this quantity with the probability of existence of the edges exhibits intriguing oscillatory behavior in order to perform our analysis we introduce a different way of computing the distribution of distances between nodes our method outperforms previous similar analyses and leads to estimates that coincide remarkably well with numerical simulations it allows us to characterize the phase transitions appearing when the connectivity probability varies

well posedness for solid liquid phase transitions with a fourth order nonlinearity abstract a phase field system which describes the evolution of both the absolute temperature and the phase variable f during first order transitions in thermal insulators is considered a thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law by virtue of the special form of the internal energy a third order nonlinearity g 2 f appears in the energy balance in place of the customarily constant latent heat as a consequence the bounds 0 f 1 hold whenever is positive valued in addition a nonlinear fourier law with conductivity proportional to temperature is assumed well posedness for the resulting initial and boundary value problem are then established in a suitable setting

feedback stabilization of a timoshenko beam with an end mass the boundary feedback control problem of a timoshenko beam with an end mass is studied in this paper first under some nonlinear boundary feedback controls the asymptotic stability for the corresponding closed loop system is shown then with the energy perturbed approach it is proved under some specific linear feedback controls applied to the tip that the vibration of the beam decays uniformly finally in the case when feedback controls are applied to both the beam ends the uniform decay is also established

the stability number of the timoshenko system with second sound abstract in this work we consider the timoshenko beam model with second sound we introduce a new number 0 that characterizes the exponential decay we prove that the corresponding semigroup associated to the system is exponentially stable if and only if 0 0 otherwise there is a lack of exponential stability in this case we prove that the semigroup decays as t 1 2 moreover we show that the rate is optimal

retrieving topological information for phase field models the phase field approach has become a popular tool in modeling interface motion microstructure evolution and more recently the shape transformation of vesicle membranes under elastic bending energy while it is advantageous to employ phase field models in numerical simu lations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes detecting topological events may also become important for many applications such as those in the simulation of blood cells motivated by such considerations a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events it can also be used as a control method to avoid unphys ical changes of topology due to the numerical methods should it become necessary for particular practical applications through numerical experiments we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes

continuity of the temperature in the two phase stefan problem the classical two phase stefan problem a model for ice water melting gives rise to a singular nonlinear partial differential equation which admits a unique weak solution here we prove that this solution and therefore the temperature in the stefan problem are continuous

on a navier stokes allen cahn model with inertial effects abstract a mathematical model describing the flow of two phase fluids in a bounded container is considered under the assumption that the phase transition is influenced by inertial effects the model couples a variant of the navier stokes system for the velocity u with an allen cahn type equation for the order parameter relaxed in time in order to introduce inertia at the microscopic level the resulting model is characterized by second order material derivatives which constitute the main difficulty in the mathematical analysis in order to obtain a tractable problem a viscous relaxation term is then included in the phase equation the mathematical results consist in existence of weak solutions in 3d and under additional assumptions existence and uniqueness of strong solutions in 2d a partial characterization of the long time behavior of solutions is also given and in particular some issues related to dissipation of energy are discussed

strong asymptotic convergence of evolution equations governed by maximal monotone operators with tikhonov regularization abstract we consider the tikhonov like dynamics u t a u t e t u t where a is a maximal monotone operator on a hilbert space and the parameter function e t tends to 0 as t with 0 e t d t when a is the subdifferential of a closed proper convex function f we establish strong convergence of u t towards the least norm minimizer of f in the general case we prove strong convergence towards the least norm point in a 1 0 provided that the function e t has bounded variation and provide a counterexample when this property fails

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

asymptotic behavior of solutions to a class of nonlinear evolution equations on etudie les equations de la chaleur a controle de temperature a l interieur ou sur la frontiere du domaine pour cela on considere un type de problemes variationnels paraboliques avec obstacles

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

weak solution of a stochastic 3d cahn hilliard navier stokes model driven by jump noise abstract we investigate a stochastic 2d and 3d cahn hilliard navier stokes system with a multiplicative noise of levy type the model consists of the navier stokes equations for the velocity coupled with a cahn hilliard system for the order phase parameter we prove that the system the existence of weak martingale solution for both 2d and 3d cases the proof of the existence is based on a classical galerkin approximation as well as some compactness methods in the 2d case we prove the pathwise uniqueness of the weak solution

some convergence results for a class of nonlinear phase field evolution equations two heat diffusion problems in the framework of the parabolic phase field model are presented the first problem is related to a single isotropic fluid and the other describes the heat transmission between two different substances in contact some known existence and uniqueness results are briefly recalled then an asymptotic analysis of both situations is carried out as the kinetic equation collapses to a temperature phase relation of stefan type in the first case in the whole material and in the second in only one of the substances in both cases a convergence result for the solutions is proved the second problem shows some more mathematical difficulties that are due to the presence of nontrivial terms on the common boundary in order to control the latter some tools are used from the convergence theory for convex functionals

the phase field method in the sharp interface limit the phase field pf method for solidification phenomena is an open formulation based on a free energy functional two common choices for the pf potential here referred to briefly as the caginalp and kobayashi models are compared with respect to their numeric results within the classical sharp interface limit both qualitative and quantitative behavior are addressed and an assessment of the computational effort required to approximate a sharp interface problem is made it is shown that the specific form of the free energy potential does have a strong influence on the convergence of the pf results to their sharp interface limit compliance of the pf solutions with the linear kinetic model for the interface temperature is also investigated a simple one dimensional solidification problem in the presence of kinetic undercooling is solved by the pf model and also by a deforming grid method our results support the view that if care is exercised in formulating the phase temperature coupling there is a high degree of confidence in using the pf method for the numerical modeling of general solidification phenomena

boundary stabilization of solutions of a nonlinear system of timoshenko type in this paper we are concerned with a multidimensional timoshenko system subjected to boundary conditions of memory type we establish general rate decay results the usual exponential and polynomial decay rates are only special cases

the phase field transition system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity abstract the paper establishes the existence estimate uniqueness and regularity for the solution of a nonlinear parabolic system a two phase caginalp type system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity it extends the already studied types of boundary conditions which makes the mathematical model to be richer and more flexible to describe the real physical phenomena including phase separation

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

feedback stabilization of rotating timoshenko beam with adaptive gain the problem of boundary feedback stabilization of rotating timoshenko beam arising from control of flexible robot arms is studied in this paper first under gain adaptive direct strain feedback controls a counterexample is given to show that the corresponding closed loop system is not asymptotically stable which is contrary to traditional conjecture the counterexample given in this paper also exemplifies an interesting result certain two two order linear partial differential equations with five homogeneous boundary conditions have non trivial solutions then with an additional boundary feedback control the related energy of the closed loop system is proved to be strongly stable or more precisely the configuration of the beam can be exponentially stabilized with some suitable non linear boundary feedback controls with adaptive gain

shape instabilities and pattern formation in solidification a new method for numerical solution of the moving boundary problem abstract when a solidification front is advancing into a region of supercooled liquid its shape is subject to instabilities which can lead to complex modes of growth the evaluation of the growth pattern is determined by the interaction of the driving force of the instability due to heat diffusion with the restabilizing force due to surface tension and its full development is a highly nonlinear process a new method for solving the two phase heat diffusion problem under these conditions is described the method is based on a single domain treatment weak formulation of the moving boundary problem with the temperature field near the interface approximated by a piecewise linear function in the spirit of the finite element technique calculated results for a model problem are in excellent agreement with the predictions of an analytical approximation

reconstruction of two time independent coefficients in an inverse problem for a phase field system abstract in this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain r n for the dimension n 3 with a single observation on a subdomain and the sobolev norm of certain partial derivatives of the solutions at a fixed positive time 0 t over the whole spatial domain the proof of these results relies on an appropriate carleman estimate for the phase field system

existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary in this article we study the degenerate system r 1 r 2 0 subject to memory conditions on the boundary given email protected 1 x u t email protected email protected u v email protected 0 r 2 x v t email protected a u v email protected 0 email protected 0 email protected 0 tg 1 t s email protected email protected s email protected 1x 0 email protected 0 email protected 0 tg 2 t s email protected email protected s email protected 1x 0 u 0 v 0 u 0 v 0 r 1u t 0 r 2v t 0 r 1u 1 r 2v 1 email protected where w is a bounded region in r n whose boundary is partitioned into disjoint sets c 0 c 1 we prove that the dissipations given by the memory terms are strong enough to guarantee exponential or polynomial decay provided the relaxation functions also decay exponentially or polynomially and with the same rate of decay

exponential attractors for a conserved phase field system with memory we consider a conserved phase field system of caginalp type characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient respectively the model consists of a parabolic integrodifferential equation coupled with a fourth order evolution equation for the phase field this system supplemented with suitable boundary conditions can be interpreted as a dissipative dynamical system in a proper phase space in a previous joint work the last two authors have proved the existence of a global attractor of finite fractal dimension here we show the existence of an exponential attractor by means of the techniques we developed for nonconserved phase field systems with memory

on a model of phase relaxation for the hyperbolic stefan problem in this paper we study a model of phase relaxation for the stefan problem with the cattaneo maxwell heat flux law we prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the stefan problem as the two relaxation parameters go to zero provided a relation between these parameters holds

analysis of an iterative scheme of fractional steps type associated to the reaction diffusion equation endowed with a general nonlinearity and cauchy neumann boundary conditions abstract the paper studies the existence uniqueness regularity and the approximation of solutions to the reaction diffusion equation endowed with a general nonlinear regular potential and cauchy neumann boundary conditions the convergence and error estimate results for an iterative scheme of fractional steps type associated to the nonlinear parabolic equation are also established the advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of nonlinear parabolic equation

uniform decay in a timoshenko type system with past history abstract fernandez sare and rivera h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502 considered the following timoshenko type system 1 t t k x x 0 2 t t b x x 0 g t x x t s d s k x 0 where g is a positive differentiable exponentially decaying function they established an exponential decay result in the case of equal wave speed propagation and a polynomial decay result in the case of nonequal wave speed propagation in this paper we study the same system for g decaying polynomially and prove polynomial stability results for the equal and nonequal wave speed propagation our results are established under conditions on the relaxation function weaker than those in h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502

decay estimate and asymptotic profile for a plate equation with memory abstract in this paper the initial value problem for a plate equation with a memory is considered under weaker assumptions on the memory function we obtain the decay estimates of solutions which is of the regularity loss type by applying the energy method in fourier space moreover if the memory kernel is an exponential function we derive the large time behavior and asymptotic profile of solutions in the one dimensional space by virtue of the technique of spectral analysis

global smooth solutions to a thermodynamically consistent model of phase field type in higher space dimensions abstract in a recent paper penrose and fife proposed a thermodynamically consistent model of phase field type for phase transition phenomena such as liquid solid phase transitions the model is based on the observation that the second law of thermodynamics postulates that the entropy functional cannot decrease along solution paths it turns out that the resulting field equations form a system of partial differential equations which is considerably more difficult than the phase field equations studied by caginalp and others for one space dimension global existence uniqueness and asymptotic behaviour of smooth solutions of the initial boundary value problem with neumann boundary data have been obtained in a recent paper by zheng in this paper we prove global existence and uniqueness in three space dimensions for the initial boundary value problem with a third boundary condition

asymptotic behavior of nonautonomous monotone and subgradient evolution equations in a hilbert setting h we study the asymptotic behavior of the trajectories of nonautonomous evolution equations dot x t a t x t ni 0 where for each t geq 0 a t h rightrightarrows h denotes a maximal monotone operator we provide general conditions guaranteeing the weak ergodic convergence of each trajectory x cdot to a zero of a limit maximal monotone operator a infty as the time variable t tends to infty the crucial point is to use the brezis haraux function or equivalently the fitzpatrick function to express at which rate the excess of mathrm gph a infty over mathrm gph a t tends to zero this approach gives a sharp and unifying view of this subject in the case of operators a t partial phi t which are subdifferentials of proper closed convex functions phi t we show convergence results for the trajectories then we specialize our results to multiscale evolution equations and obtain asymptotic properties of hierarchical minimization and selection of viscosity solutions illustrations are given in the field of coupled systems and partial differential equations

a phase field model with temperature dependent constraint this paper is concerned with a phase field model with temperature dependent constraint for the order parameter in the kinetic equation of the order parameter we take account of diffusion as well as undercooled superheated state which is modelled by means of a hysteresis input output relation the input is the temperature field and the output is the order parameter in this paper we shall show that there exists a solution globally in time in a physically reasonable sense when the coefficient of interfacial energy is sufficiently small

on the existence uniqueness and regularity of solutions to the phase field system with a general regular potential and a general class of nonlinear and non homogeneous boundary conditions abstract this paper studies a caginalp phase field transition system endowed with a general regular potential as well as a general class in both unknown functions of nonlinear and non homogeneous depending on time and space variables boundary conditions we first prove the existence uniqueness and regularity of solutions to the allen cahn equation subject to the nonlinear and non homogeneous dynamic boundary conditions the existence uniqueness and regularity of solutions to the caginalp system in this new formulation are also proved this extends previous works concerned with regular potential and nonlinear boundary conditions allowing the present mathematical model to better approximate the real physical phenomena especially phase transitions

global existence and asymptotic decay of solutions to the nonlinear timoshenko system with memory abstract in this paper we consider the initial value problem for the nonlinear timoshenko system with a memory term due to the regularity loss property and weak dissipation we have to assume stronger nonlinearity than usual by virtue of the semi group arguments we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data where we employ a time weighted l 2 energy method combined with the optimal l 2 decay of lower order derivatives of solutions

on generalized windmill graphs abstract in this paper we will consider generalizations of the class of so called windmill graphs which were recently introduced by estrada 6 a windmill graph w k consists of copies of the complete graph k k with every node connected to a common node estrada 6 showed that the clustering coefficient and the transitivity index of windmill graphs diverge when the graph size tends to infinity in addition 6 studied the spectra of the adjacency and the laplacian matrices of these graphs in this paper we will generalize the family of windmill graphs in three ways we will study properties for all three types of generalized windmill graphs in particular we will focus on the behavior of the two clustering metrics we will quantify the difference between the two metrics under various conditions in addition we give the spectra of the adjacency and the laplacian matrices of these graphs we will also derive analytic expressions for several other graph metrics such as average path length heterogeneity index and a variety of robustness metrics we also show how the generalized windmill graphs can be used to construct pairs of non isomorphic graphs with the same number of nodes and links finally we will show how generalized windmill graphs occur quite naturally in the study of public transportation networks

the numerical computation of heteroclinic connections in systems of gradient partial differential equations the numerical computation of heteroclinic connections in partial differential equations pdes with a gradient structure such as those arising in the modeling of phase transitions is considered initially a scalar reaction diffusion equation is studied structural assumptions are made on the problem to ensure the existence of absorbing sets and consequently a global attractor as a result of the gradient structure it is known that if all equilibria are hyperbolic the global attractor comprises the set of equilibria and heteroclinic orbits connecting equilibria to one another thus it is natural to consider direct approximation of the set of equilibria and the connecting orbits results are proved about the fourier spanning basis for branches of equilibria and also for certain heteroclinic connections these results exploit the oddness of the nonlinearity the reaction diffusion equation is then approximated by a galerkin spectral discretization to produce a system of ordinary differential equations

asymptotic behaviour of solutions to parabolic elliptic variational inequalities in a real hilbert space h where j is a given interval in r 0 co j is the subdifferential of a convex function 4 on h and b is a maximal monotone operator in h the abstract setting reflects the form of a class of parabolic elliptic boundary value problems with time dependent obstacles such problems arise in particular as mathematical models of various processes in electrochemical technology and some flows with saturations in porous media time dependent obstacles may represent geometric controls moving control actions in these problems in particular such controls may be comprehended in variable boundary conditions prescribed over time dependent parts of the boundary of domain or in source terms distributed over time dependent subdomains the former refers to control of flows via variable water table in reservoirs the latter characterizes control of electrochemical process via mechanically driven motion of a toolpiece cathode the most typical control objective consists there in stabilizing the state of the process at a given spatial distribution for example constant water head and desired shape of anode this motivates our interest in the asymptotic behavior of solutions to the corresponding boundary value problems as t a to the knowledge of the authors this question has so far not been studied in literature as it has been shown in kenmochi pawlow 16 171 the class of considered time dependent problems admits a representation in the form of evolution equation e b in 16 171 the corresponding results on existence uniqueness and stability of solutions have been established in the present paper we study the asymptotic properties of solutions to e c b as t 00 provided some hypotheses are imposed on the family t e r and the limit 4 of as t a for the solution u u of e d b on r we prove that

the frequency localization technique and minimal decay regularity for euler maxwell equations abstract dissipative hyperbolic systems of regularity loss have been recently received increasing attention extra higher regularity is usually assumed to obtain the optimal decay estimates in comparison with the global in time existence of solutions in this paper we develop a new frequency localization time decay property which enables us to overcome the technical difficulty and improve the minimal decay regularity for dissipative systems as an application it is shown that the optimal decay rate of l 1 r 3 l 2 r 3 is available for euler maxwell equations with the critical regularity s c 5 2 that is the extra higher regularity is not necessary

abstract approach to evolution equations of phase field type and applications a general system of abstract nonlinear parabolic equations deriving from phase field models of heat transfer in anisotropic fluids with phase transitions is studied through a backward finite differences approximation scheme and existence and uniqueness theorems are proved then applications are presented to two physical situations first a standard heat diffusion problem is briefly discussed mainly as a justification of the choices of the abstract setting second a more interesting transmission problem between two different adjoining fluids is studied under very general compatibility hypotheses and the abstract results are adapted to provide an existence and uniqueness theorem also in this case moreover through convex analysis techniques it is performed a mathematical study of the subdifferential type relations linking the phase fields and the temperatures to the internal energies of the fluids email schimper dragon ian pv cnr it keywords phase field models subdifferential operators abstract evolution equations

global existence asymptotic behavior and uniform attractors for a non autonomous timoshenko system of thermoelasticity of type iii with a time varying delay abstract in this paper we first establish the global existence by using the variable norm technique of kato and semigroup method second under suitable assumptions on the data we obtain the asymptotic behavior of the solution last we prove the existence of a uniform attractor by using the method of uniform contractive functions

local minimisers and singular perturbations we construct local minimisers to certain variational problems the method is quite general and relies on the theory of convergence the approach is demonstrated through the model problem it is shown that in certain nonconvex domains n and for e small there exist nonconstant local minimisers u e satisfying u e 1 except in a thin transition layer the location of the layer is determined through the requirement that in the limit u e u 0 the hypersurface separating the states u 0 1 and u 0 1 locally minimises surface area generalisations are discussed with for example vector valued u and anisotropic perturbations replacing u 2

variational inequalities for a system of elliptic parabolic equations abstract we create a general framework for mathematical study of variational inequalities for a system of elliptic parabolic equations in this paper we establish a solvability theorem concerning the existence of solutions for the vector valued elliptic parabolic variational inequality with time dependent constraint moreover we give some applications of the system for example time dependent boundary obstacle problem and time dependent interior obstacle problem

global well posedness and polynomial decay for a nonlinear timoshenko cattaneo system under minimal sobolev regularity abstract we consider the nonlinear stability of the timoshenko cattaneo system in the one dimensional whole space the timoshenko system consists of two coupled wave equations with non symmetric relaxation and describes vibrations of the beam with shear deformation and rotational inertia effect generally if the relaxation is not symmetric the dissipation is produced through the complicated interaction of the components of the system and their decay estimates and the energy estimates are of regularity loss type in this paper we introduce the mathematical method to control such a weak dissipativity by investigating the timoshenko system with cattaneo s law which is the first order approximation of fourier s law with its time delay effect racke said houari 2012 showed the global existence and the decay estimate of solutions by assuming high regularity h 8 l 1 on the small initial data to control their weak dissipativity in contrast we prove the global existence in h 2 by energy methods without any negative weights our regularity assumption is the same as that needed to show the local existence that is we do not need to assume the extra higher regularity on the initial data besides the optimal decay estimate in h 2 l 1 is shown by using the time decay inequality of l p l q l r type

on uniform decay of coupled wave equation of kirchhoff type subject to memory condition on the boundary abstract in this paper we prove the existence of solution and uniform decay of energy to the mixed problem for coupled wave equation of kirchhoff type subject to memory condition on the boundary

phase field systems with nonlinear coupling and dynamic boundary conditions we consider phase field systems of caginalp type on a three dimensional bounded domain the order parameter fulfills a dynamic boundary condition while the relative temperature is subject to a homogeneous boundary condition of dirichlet neumann or robin type moreover the two equations are nonlinearly coupled through a quadratic growth function here we extend several results which have been proven by some of the authors for the linear coupling more precisely we demonstrate the existence and uniqueness of global solutions then we analyze the associated dynamical system and we establish the existence of global as well as exponential attractors we also discuss the convergence of given solutions to a single equilibrium

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

a class of nonlinear elliptic parabolic equations with time dependent constraints on etudie les equations d evolutions non lineaires de la forme f t du t dt t v t v t bu t 0 t t dans un espace de hilbert h ou t est la sous differentielle d une fonction convexe t definie sur h b est un operateur monotone maximal dans h on considere l existence et l unicite des solutions ainsi que des estimations a priori

a convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming abstract we present a new result on the asymptotic behavior of nonautonomous subgradient evolution equations of the form u t t u t where t t 0 is a family of closed proper convex functions the result is used to study the flow generated by the family t x f x r t where f x r ctx r exp aix bi r is the exponential penalty approximation of the linear program min ctx ax b and r t is a positive function tending to 0 when t we prove that the trajectory u t converges to an optimal solution u of the linear program and we give conditions for the convergence of an associated dual trajectory t toward an optimal solution of the dual program

dissipative structure and global existence in critical space for timoshenko system of memory type abstract in this paper we consider the initial value problem for the timoshenko system with a memory term in one dimensional whole space in the first place we consider the linearized system applying the energy method in the fourier space we derive the pointwise estimate of the solution in the fourier space which first gives the optimal decay estimate of the solution next we give a characterization of the dissipative structure of the system by using the spectral analysis which confirms our pointwise estimate is optimal in the second place we consider the nonlinear system we show that the global in time existence and uniqueness result could be proved in the minimal regularity assumption in the critical sobolev space h 2 in the proof we don t need any time weighted norm as recent works we use just an energy method which is improved to overcome the difficulties caused by regularity loss property of timoshenko system

general energy decay in a timoshenko type system of thermoelasticity of type iii with a viscoelastic damping in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove a general decay result from which the exponential and polynomial decays are only special cases

distance sum heterogeneity in graphs and complex networks abstract the heterogeneity of the sum of all distances from one node to the rest of nodes in a graph distance sum or status of the node is analyzed we start here by analyzing the cumulative statistical distributions of the distance sum of nodes in random and real world networks from this analysis we conclude that statistical distributions do not reveal the distance sum heterogeneity in networks thus we motivate an index of distance sum heterogeneity based on a hypothetical consensus model in which the nodes of the network try to reach an agreement on their distance sum values this index is expressed as a quadratic form of the combinatorial laplacian matrix of the network the distance sum heterogeneity index g gives a natural interpretation of the balaban index for any kind of graph network we conjecture here that among graphs with a given number of nodes g is maximized for a graph with a structure resembling the agave plant we also found the graphs that maximize g for a given number of nodes and links using this index and a normalized version of it we studied random graphs as well as 57 real world networks our findings indicate that the distance sum heterogeneity index reveals important structural characteristics of networks which can be important for understanding the functional and dynamical processes in complex systems

on a system of nonlinear pde s for phase transitions with vector order parameter and convective effect the paper deals with a system of nonlinear pde s which describes a phase field model with convection and temperature dependent constraint to the vector order parameter existence of solutions for the system under consideration is proved by the method of yosida approximation and fixed point arguments

computation of sharp phase boundaries by spreading the planar and spherically symmetric cases abstract the sharp interface that arises from any of the major transition problems classical or modified stefan etc can be smoothed using the phase field approach as a numerical tool the basic idea is that the thickness of the interface can be regarded as a mathematical free parameter which can be stretched beyond its physical value for computational convenience the computations in one dimensional space and n dimensions with radial symmetry indicate that this is an efficient method for dealing with stiff equations and results in a very accurate interface determination without explicit tracking the question of optimizing the interfacial thickness with respect to grid size is also considered empirically the technique also provides a numerical verification of the concept of an unstable critical radius of solidification

core satellite graphs clustering assortativity and spectral properties abstract core satellite graphs sometimes referred to as generalized friendship graphs are an interesting class of graphs that generalize many well known types of graphs in this paper we show that two popular clustering measures the average watts strogatz clustering coefficient and the transitivity index diverge when the graph size increases we also show that these graphs are disassortative in addition we completely describe the spectrum of the adjacency and laplacian matrices associated with core satellite graphs finally we introduce the class of generalized core satellite graphs and analyze their clustering assortativity and spectral properties

energy decay in a timoshenko type system of thermoelasticity of type iii in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove the exponential stability by using the energy method

quantifying network heterogeneity despite degree distributions give some insights about how heterogeneous a network is they fail in giving a unique quantitative characterization of network heterogeneity this is particularly the case when several different distributions fit for the same network when the number of data points is very scarce due to network size or when we have to compare two networks with completely different degree distributions here we propose a unique characterization of network heterogeneity based on the difference of functions of node degrees for all pairs of linked nodes we show that this heterogeneity index can be expressed as a quadratic form of the laplacian matrix of the network which allows a spectral representation of network heterogeneity we give bounds for this index which is equal to zero for any regular network and equal to one only for star graphs using it we study random networks showing that those generated by the erdos renyi algorithm have zero heterogeneity and those generated by the preferential attachment method of barabasi and albert display only 11 of the heterogeneity of a star graph we finally study 52 real world networks and we found that they display a large variety of heterogeneities we also show that a classification system based on degree distributions does not reflect the heterogeneity properties of real world networks

a posteriori error estimates for variable time step discretizations of nonlinear evolution equations we study the backward euler method with variable time steps for abstract evolution equations in hilbert spaces exploiting convexity of the underlying potential or the angle bounded condition thereby assuming no further regularity we derive novel a posteriori estimates of the discretization error in terms of computable quantities related to the amount of energy dissipation or monotonicity residual these estimators depend solely on the discrete solution and data and impose no constraints between consecutive time steps we also prove that they converge to zero with an optimal rate with respect to the regularity of the solution we apply the abstract results to a number of concrete strongly nonlinear problems of parabolic type with degenerate or singular character 2000 john wiley sons inc

on the stabilization of timoshenko systems with memory and different speeds of wave propagation in this work we consider a one dimensional timoshenko system with different speeds of wave propagation and with only one control given by a viscoelastic term on the angular rotation equation for a wide class of relaxation functions and for sufficiently regular initial data we establish a general decay result for the energy of solution unlike the past history and internal feedback cases the second energy is not necessarily decreasing to overcome this difficulty a precise estimate of the second energy in terms of the initial data and the relaxation function is proved

asymptotic behavior of the energy for a class of weakly dissipative second order systems with memory a class of second order abstract systems with memory and dirichlet boundary conditions is investigated by suitable liapunov functionals existence of solutions as well as asymptotic behavior are determined in particular when the memory kernel decays exponentially the polynomially decay of the solutions is proved

when local and global clustering of networks diverge abstract the average watts strogatz clustering coefficient and the network transitivity are widely used descriptors for characterizing the transitivity of relations in real world graphs networks these indices are bounded between zero and one with low values indicating poor transitivity and large ones indicating a high proportion of closed triads in the graphs here we prove that these two indices diverge for windmill graphs when the number of nodes tends to infinity we also give evidence that this divergence occurs in many real world networks especially in citation and collaboration graphs we obtain analytic expressions for the eigenvalues and eigenvectors of the adjacency and the laplacian matrices of the windmill graphs using this information we show the main characteristics of two dynamical processes when taking place on windmill graphs synchronization and epidemic spreading finally we show that many of the structural and dynamical properties of a real world citation network are well reproduced by the appropriate windmill graph showing the potential of these graphs as models for certain classes of real world networks

coupling general penalty schemes for convex programming with the steepest descent and the proximal point algorithm we study the asymptotic behavior of the continuous flow generated by coupling the steepest descent method with a general class of penalty schemes for convex programming we establish convergence of the trajectories towards primal optimal solutions as well as convergence of some naturally associated dual paths the results are extended to the sequences generated by an implicit discretization scheme which corresponds to the coupling of an inexact proximal point iteration with the penalty schemes

asymptotic properties of solutions of time dependent volterra integral equations abstract the asymptotic properties of the bounded solutions of a time dependent nonlinear volterra equation are studied in a hilbert space an application of physical interest is also given

on a nonlocal phase field system abstract we study the existence uniqueness and continuous dependence on initial data of the solution to a nonlocal phase field system on a bounded domain the system is a gradient flow for a free energy functional with nonlocal interaction also we study the asymptotic behavior of the solution and show the existence of an absorbing set in some metric space