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

the moser trudinger inequality on kahler einstein manifolds we prove the conjecture of tian on the strong form of the moser trudinger inequality for k ahler einstein manifolds with positive first chern class when there are no holomorphic vector fields and more generally when the setting is invariant under a maximal compact subgroup of the automorphism group

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

remarks on the existence problem of positive kahler einstein metrics on introduit un invariant m qui donne un critere pour l existence de metriques de kahler einstein

the best constant of the moser trudinger inequality on s2 we consider the best constant of the moser trudinger inequality on s 2 under a certain orthogonality condition applying moser s calculation we construct a counterexample to the sharper inequality with the condition

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

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

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

blow up and global existence for heat flows of harmonic maps in this paper it is proved that the solution to the evolution problem for harmonic maps blows up in finite time if the initial map belongs to some nontrivial homotopy class and the initial energy is sufficiently small

a uniform stability result for thermoelasticity of type iii with boundary distributed delay abstract in this paper we consider a thermoelastic system of type iii with boundary distributed delay under suitable assumption on the weight of the delay we prove using the energy method that the damping effect through heat conduction given by green and naghdi s theory is still strong enough to uniformly stabilize the system even in the presence of time delay

the heat flow of harmonic maps from noncompact manifolds the authors consider the global existence of the heat flow of harmonic maps from noncompact manifolds while imposing restrictions on the initial data

method of lyapunov functionals construction in stability of delay evolution equations the investigation of stability for hereditary systems is often related to the construction of lyapunov functionals the general method of lyapunov functionals construction which was proposed by v kolmanovskii and l shaikhet and successfully used already for functional differential equations for difference equations with discrete time for difference equations with continuous time is used here to investigate the stability of delay evolution equations in particular partial differential equations

kahler einstein metrics with positive scalar curvature in this paper we prove that the existence of kahler einstein metrics implies the stability of the underlying kahler manifold in a suitable sense in particular this disproves a long standing conjecture that a compact kahler manifold admits kahler einstein metrics if it has positive first chern class and no nontrivial holomorphic vector fields we will also establish an analytic criterion for the existence of kahler einstein metrics our arguments also yield that the analytic criterion is satisfied on stable kahler manifolds provided that the partial c 0 estimate posed in t6 is true

convergence of the wave equation damped on the interior to the one damped on the boundary abstract in this paper we study the convergence of the wave equation with variable internal damping term n x u t to the wave equation with boundary damping x x u t when n x converges to x x in the sense of distributions when the domain in which these equations are defined is an interval in r we show that under natural hypotheses the compact global attractor of the wave equation damped on the interior converges in x h 1 l 2 to the one of the wave equation damped on the boundary and that the dynamics on these attractors are equivalent we also prove in the higher dimensional case that the attractors are lower semicontinuous in x and upper semicontinuous in h 1 e h e

exponential stability and inequalities of solutions of abstract functional differential equations abstract with the lyapunov second method we study the abstract functional differential equation d u d t f t u t we obtain inequalities of solutions and exponential stability with conditions like i w 1 u t x v t u t w 2 d t u t t h t l s w 1 u s x d s ii v 1 t u t t w 2 d t u t p t applications in ordinary and partial functional differential equations are given

global existence asymptotic stability and uniform attractors for non autonomous thermoelastic systems with constant time delay in this paper we first consider a non autonomous thermoelastic system with a boundary delay and obtain the asymptotic behavior then using the contractive function method and multiplier techniques we establish the asymptotic behavior and the existence of a uniform attractor of the system with a boundary time delay the main advantage of this method is that we only need to verify compactness condition with the type of energy estimates same as those for establishing the absorbing set moreover we investigate an alternative result of solutions to semilinear thermoelastic systems by virtue of the semigroup method

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays

an analysis of delay dependent stability for ordinary and partial differential equations with fixed and distributed delays this paper is concerned with the study of the stability of ordinary and partial differential equations with both fixed and distributed delays and with the study of the stability of discretizations of such differential equations we start with a delay dependent asymptotic stability analysis of scalar ordinary differential equations with real coefficients we study the exact stability region of the continuous problem as a function of the parameters of the model next it is proved that a time discretization based on the trapezium rule can preserve the asymptotic stability for the considered set of test problems in the second part of the paper we study delay partial differential equations the stability region of the fully continuous problem is analyzed first then a semidiscretization in space is applied it is shown that the spatial discretization leads to a reduction of the stability region when the standard second order central difference operator is employed to approximate the diffusion operator finally we consider the delay dependent stability of the fully discrete problem where the partial differential equation is discretized both in space and in time some numerical examples and further discussions are given