uniform decay for the unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping in this article we study the existence of solutions and the uniform decay rate of the energy for nonlinear unilateral problem associated to the kirchhoff type wave equations with nonlinear boundary damping to obtain the existence of solutions we make use of faedo galerkin s approximation and also to show the uniform stabilization we use the perturbed energy method

prescribing the center of mass of a multi soliton solution for a perturbed semilinear wave equation abstract we construct a finite time blow up solution for a class of strongly perturbed semilinear wave equation with an isolated characteristic point in one space dimension given any integer k 2 and 0 r we construct a blow up solution with a characteristic point a such that the asymptotic behavior of the solution near a t a shows a decoupled sum of k solitons with alternate signs whose centers in the hyperbolic geometry have 0 as a center of mass for all times although the result is similar to the unperturbed case in its statement our method is new indeed our perturbed equation is not invariant under the lorentz transform and this requires new ideas in fact the main difficulty in this paper is to prescribe the center of mass 0 r we would like to mention that our method is valid also in the unperturbed case and simplifies the original proof by cote and zaag 9 as far as the center of mass prescription is concerned

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

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

global existence and nonexistence for nonlinear wave equations with damping and source terms we consider an initial boundary value problem for a nonlinear wave equation in one space dimension the nonlinearity features the damping term u m 1 u t and a source term of the form u p 1 u with m p 1 we show that whenever m p then local weak solutions are global on the other hand we prove that whenever p m and the initial energy is negative then local weak solutions cannot be global regardless of the size of the initial data

stable and unstable sets for the cauchy problem for a nonlinear wave equation with nonlinear damping and source terms for the cauchy problem for the nonlinear wave equation with nonlinear damping and source terms we define stable and unstable sets for the initial data we prove that if during the evolution the solution enters into the stable set the solution is global and we are able to estimate the decay rate of the energy if during the evolution the solution enters into the unstable set the solution blows up in finite time

global existence and finite time blow up for a class of semilinear wave equations on r n abstract in this paper we consider the initial value problem for a class of semilinear wave equations with damping and source terms under certain conditions we establish the global existence of solutions and the asymptotic behavior of the solutions by introducing an appropriate lyapunov functions moreover we examine the blow up in finite time when the initial data is sufficiently large

on uniform decay of the solution for a damped nonlinear coupled system of wave equations with nonlinear boundary damping and memory term in this paper we are concerned with the existence and energy decay of the solution to the initial boundary value problem for the nonlinear coupled wave equations with nonlinear boundary damping and memory term

long time asymptotic expansion for the damped semilinear wave equation the first initial boundary value problem is considered for the damped semilinear wave equation with the quadratic nonlinearity for small initial data and homogeneous boundary conditions its solution is constructed in the form of a series in the eigenfunctions of the laplace operator the long time asymptotic expansion is obtained which shows the nonlinear effects of amplitude and frequency multiplication the same results hold for the admissible initial data that are not small

global existence and energy decay result for a weak viscoelastic wave equations with a dynamic boundary and nonlinear delay term in this paper we consider the weak viscoelastic wave equation u t t u u t t 0 t g t s u s d s u p 2 u with dynamic boundary conditions and nonlinear delay term first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem secondly we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time in using the concept of stable sets finally by exploiting the perturbed lyapunov functionals we extend and improve the previous result from gerbi and said houari 2011

explosion of solutions to nonlinear stochastic wave equations with multiplicative noise abstract let d r d be an open bounded domain in the d dimensional euclidian space r d with smooth boundary d in this paper we investigate the local existence global existence and explosion of solutions to the following stochastic wave equation 0 1 d x t y t d t d y t x t y t p y t x t q x t d t b t x t y t d w t p q 0 x 0 x 0 y 0 y 0 x t d 0 where 2 x i 2 is a laplace operator the process w t denotes a cylindrical brownian process on a complete probability space f p with filtration of the usual condition

global existence and uniform decay for wave equation with dissipative term and boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation u t email protected b x u t f u 0 in bounded domains with nonlinear damped boundary conditions given by email protected email protected g u t 0 with restrictions on function f u g u t and b x we prove the existence by means of the glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of kmornik and zuazua see 7

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

global existence to the initial boundary value problem for a system of semilinear wave equations abstract we prove the global existence of finite energy and h 2 solutions for a system of nonlinear wave equations in a bounded domain one equation of the system has a dissipative term while another equation has no dissipative mechanism to derive the delicate a priori estimates we employ a loan method

existence uniqueness and blowup for hyperbolic equations with nonstandard growth conditions in this paper we consider the following problem utt u b x t u x t 2u f x t x t qt 0 t u x 0 u0 x ut x 0 u1 x 0 x u t 0 t 0 t under conditions 0 b t b x t b t 0 b t b x t b t 1 t x t t 1 t x t t we study the existence and uniqueness of weak and strong solutions we prove the blowup of nonnegative solutions also we consider the blowup effect for a more generalized problem utt lu f x t u inqt u x 0 u0 x in ut x 0 u1 x in u 0on t where ll is the linear elliptic operator lu di aij x dju ai x u a0 x u lu di aij x dju ai x u a0 x u and the right hand side has the form f x t u k 1nbk x t u k x t 1 i nkci x t di s t u i s t 1ds with bk 0bk 0 ci 0ci 0 di 0di 0

local and global wellposedness of weak solutions for the wave equation with nonlinear boundary and interior sources of supercritical exponents and damping abstract we consider the wave equation with interior and boundary nonlinear sources and damping and we are interested in local and global wellposedness of finite energy solutions the main difficulty is represented by the fact that the lopatinski condition fails to hold unless the dim 1 and thus the analysis of the boundary nonlinearities becomes a subtle issue

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

on behaviour of solutions for a nonlinear viscoelastic equation with variable exponent nonlinearities abstract this paper deals with a viscoelastic wave equation with variable exponent nonlinearities subject to nonlinear boundary feedback under appropriate conditions a general decay result associated to solution energy is proved it is also shown that regarding arbitrary positive initial energy solutions blow up in a finite time

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

lifespan of solutions to the damped wave equation with a critical nonlinearity abstract in the present paper we study a lifespan of solutions to the cauchy problem for semilinear damped wave equations dw t 2 u u t u f u t x 0 t e r n u 0 x e u 0 x x r n t u 0 x e u 1 x x r n where n 1 f u u p 1 u or u p p 1 e 0 is a small parameter and u 0 u 1 is a given initial data the main purpose of this paper is to prove that if the nonlinear term is f u u p and the nonlinear power is the fujita critical exponent p p f 1 2 n then the upper estimate to the lifespan is estimated by t e exp c e p for all e 0 1 and suitable data u 0 u 1 without any restriction on the spatial dimension our proof is based on a test function method utilized by zhang 35 we also prove a sharp lower estimate of the lifespan t e to dw in the critical case p p f

global existence and uniform stabilization of a generalized dissipative klein gordon equation type with boundary damping in this paper we prove the existence uniqueness and uniform stability of strong and weak solutions of the nonlinear generalized klein gordon equation 1 1 1 see sec i in bounded domains with nonlinear damped boundary conditions given by 1 1 3 see sec i with some restrictions on function f u h u g ut and b x we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique

approximation of nonlinear wave equations with nonstandard anisotropic growth conditions weak solutions for nonlinear wave equations involving the p x laplacian for p 1 are constructed as appropriate limits of solutions of an implicit finite element discretization of the problem a simple fixed point scheme with appropriate stopping criteria is proposed to conclude convergence for all discretization regularization perturbation and stopping parameters tending to zero computational experiments are included to motivate interesting dynamics such as blowup and asymptotic decay behavior

local hadamard well posedness for nonlinear wave equations with supercritical sources and damping abstract we consider the wave equation with supercritical interior and boundary sources and damping terms the main result of the paper is local hadamard well posedness of finite energy weak solutions the results obtained 1 extend the existence results previously obtained in the literature by allowing more singular sources 2 show that the corresponding solutions satisfy hadamard well posedness conditions during the time of existence this result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping

global solutions to a structure acoustic interaction model with nonlinear sources abstract this article focuses on a structural acoustic interaction system consisting of a semilinear wave equation defined on a smooth bounded domain r 3 which is strongly coupled with a berger plate equation acting only on a flat part of the boundary of in particular the source terms acting on the wave and plate equations are allowed to have arbitrary growth order we employ a standard galerkin approximation scheme to establish a rigorous proof of the existence of local weak solutions in addition under some conditions on the parameters in the system we prove such solutions exist globally in time and depend continuously on the initial data

discontinuous galerkin methods for the stokes equations with nonlinear damping term on general meshes abstract this paper presents the interior penalty discontinuous galerkin ipdg methods to solve the stationary stokes equations with nonlinear damping term the ipdg discrete schemes are established on general meshes the corresponding consistency and stabilization of those schemes are proved subsequently we analyze the existence boundedness and uniqueness of the discrete solutions then the optimal error estimates are derived in the l 2 norm and h 1 like dg norm for the velocity variable and l 2 norm for the pressure variable respectively finally some numerical experiments in two dimensional are reported to demonstrate the theoretical results and show the robustness of our discrete schemes

blow up results for some second order hyperbolic inequalities with a nonlinear term with respect to the velocity we give sufficient conditions on the initial data so that a semilinear wave inequality blows up in finite time our method is based on the study of an associated second order differential inequality the same method is applied to some semilinear systems of mixed type

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

blow up at infinity of solutions for integro differential equation in this paper we consider the blow up at infinity of solutions for the integro differential equation with strong damping term as well as a time dependent nonlinear dissipative function q and a driving force term f under the homogeneous dirichlet boundary conditions some interesting applications are given in particular subcases of q and f this improves earlier results in the literatures

weak solutions and blow up for wave equations of p laplacian type with supercritical sources this paper investigates a quasilinear wave equation with kelvin voigt damping utt pu ut f u in a bounded domain 3 and subject to dirichlet boundary conditions the operator p 2 p 3 denotes the classical p laplacian the nonlinear term f u is a source feedback that is allowed to have a supercritical exponent in the sense that the associated nemytskii operator is not locally lipschitz from w01 p into l2 under suitable assumptions on the parameters we prove existence of local weak solutions which can be extended globally provided the damping term dominates the source in an appropriate sense moreover a blow up result is proved for solutions with negative initial total energy

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 the laplace equation with non linear dynamical boundary conditions the main part of the paper deals with local existence and global existence versus blow up for solutions of the laplace equation in bounded domains with a non linear dynamical boundary condition more precisely we study the problem consisting in 1 the laplace equation in 0 infty times omega 2 a homogeneous dirichlet condition 0 infty times gamma 0 3 the dynamical boundary condition frac partial u partial nu u t m 2 u t u p 2 u on 0 infty times gamma 1 4 the initial condition u 0 x u 0 x on partial omega here omega is a regular and bounded domain in mathbb r n with n ge 1 and gamma 0 and gamma 1 endow a measurable partition of partial omega moreover m 1 2 le p r where r 2 n 1 n 2 when n ge 3 r infty when n 1 2 and u 0 in h 1 2 partial omega u 0 0 on gamma 0 the final part of the paper deals with a refinement of a global non existence result by levine park and serrin which is applied to the previous problem

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

on uniform decay of solutions for wave equation of kirchhoff type with nonlinear boundary damping and memory source term in this paper we prove the existence of solution to the mixed problem for wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of solution

conformal metrics with prescribed gaussian curvature on s2 we consider on s 2 the problem of which functions k can be the scalar curvature of a metric conformal to the standard metric on s 2 we assume that k is a function of one variable and we obtain a necessary and sufficient condition for the problem to be solvable we also obtain several new sufficient conditions on k which are easy to check in order that the problem be solvable

uniform decay of solutions for a quasilinear system of viscoelastic equations abstract in this paper we consider a system of two coupled quasilinear viscoelastic equations in canonical form with dirichlet boundary condition we use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay with exponential and polynomial rates of the solutions energy which extends some existing results for a single equation to the case of a coupled system

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

regularity of higher energies of wave equation with nonlinear localized damping and a nonlinear source abstract wave equation driven by a nonlinear dissipative source and subjected to a nonlinear damping that is localized on a small region near the boundary is considered while finite energy h 1 l 2 solutions to this problem are bounded uniformly for all times t 0 this property generally fails for higher energy norms h 2 h 1 this is due to a generation of higher energy by the source and the ultimate loss of dissipativity however the presence of the damping may turn things around by counteracting the sources also at the higher energy levels the benefits of this counteraction depend on the nonlinear characteristics of dissipation any deviation from linearity be it origin or infinity causes degradation of the damping hence of decay rates of finite energy this in turn is shown to have an adverse effect on the stability of higher energies the main aim of this paper is to provide a quantitative analysis of the interaction between nonlinearity of the damping and nonlinearity of the source we show that under some correlation between growth rates of the damping and the source the norms of topological order above the finite energy level remain globally bounded for all times

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

cauchy problem for a nonlinear wave equation with nonlinear damping and source terms here a b 0 and p 1 m 1 in case of ibvp in a bounded domain rn with dirichlet boundary conditions the following results are known 1 when a 0 it is proved see 1 3 8 14 16 that the solution blows up in nite time for su ciently large initial data 2 when b 0 haraux and zuazua 5 and kopackova 7 prove the global existence result for large initial data the behavior of the solution of eq 1 1 with nonlinear source and linear damping case m 1 in an abstract setting was considered by levine in 9 more precisely he showed that the solutions with negative initial energy are nonglobal

nonlinear damped wave equation in this paper we consider the following nonlinear wave equation with variable exponents uttu aut ut m 2 bu u p 2 where a b are positive constants by using the faedogalerkin method the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p we also prove the finite time blow up of solutions and give a two dimension numerical example to illustrate the blow up result

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

superclose and superconvergence of finite element discretizations for the stokes equations with damping a class of conforming mixed finite element methods fems are applied to the stokes equations with damping with the help of the prior estimates for the exact and approximated solutions and the appropriate choice of the parameters a n and r appeared in the problem the superclose and superconvergence results for the velocity in h 1 norm and the pressure in l 2 norm are derived to our best knowledge this is the first superconvergence analysis of conforming mixed fems for this kind nonlinear problem

blow up for nonlinear dissipative wave equations in rn abstract we consider the cauchy problem u t t u u t m 1 u t u p 1 u t x 0 r n u 0 x u 0 x u t 0 x v 0 x for 1 m p p n n 2 for n 3 we prove that for any given numbers 0 0 there exist infinitely many data u 0 v 0 in the energy space such that the initial energy e 0 the gradient norm u 0 2 and the solution of the above cauchy problem blows up in finite time

blow up of positive initial energy solutions of a nonlinear viscoelastic hyperbolic equation abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u t m 2 u u p 2 with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g and for p m we prove that there are solutions with positive initial energy that blow up in finite time

on decay and blow up of solutions for a system of nonlinear wave equations abstract the initial boundary value problem for a system of viscoelastic wave equations of kirchhoff type with the nonlinear damping and the source terms in a bounded domain is considered we prove that under suitable conditions on the nonlinearity of the damping and the source terms and certain initial data in the stable set and for a wider class of relaxation functions the decay estimates of the energy function is exponential or polynomial depending on the exponents of the damping terms in both equations by using nakao s method conversely for certain initial data in the unstable set we obtain the blow up of solutions in finite time when the initial energy is nonnegative this improves earlier results in the literature

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

energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms abstract in this paper we develop an intrinsic approach to derivation of energy decay rates for the semilinear wave equation with localized interior nonlinear monotone damping g u t and a source term f u the proposed approach allows to consider in an unified way much more general classes of hyperbolic problems than addressed before in the literature these generalizations refer to both geometric and topological aspects of the problem the method leads to optimal decay rates for solutions of semilinear hyperbolic equations driven by a source of critical exponent and subjected to a nonlinear damping localized in a small region adjacent to a portion of the boundary the distinct features of the model include i neumann boundary conditions are assumed and ii no growth conditions are imposed on the damping g s it is well known that neumann boundary does not satisfy lopatinski condition and therefore the analysis of propagation of energy in the absence of the damping on the neumann part of the boundary requires special geometric considerations in addition the sole conditions assumed on g s are monotonicity continuity and g 0 0 in particular no differentiability and no growth conditions are imposed on the damping both at the origin and at the infinity the asymptotic decay rates for the energy function are obtained from an intrinsic algorithm driven by solutions of simple ode several examples illustrate the theory by exhibiting various decay rates exponential algebraic rational logarithmic etc for the energy functional an important corollary of our energy decay theorem is a stability result which shows that under certain conditions when dissipation is sublinear at infinity the solution of the system remains uniformly bounded for all time in the norms above the finite energy level even in the presence of a nonlinear source term

blow up of solutions for some non linear wave equations of kirchhoff type with some dissipation abstract the initial boundary value problem for non linear wave equations of kirchhoff type with dissipation in a bounded domain is considered we prove the blow up of solutions for the strong dissipative term u t and the linear dissipative term u t by the energy method and give some estimates for the life span of solutions we also show the nonexistence of global solutions with positive initial energy for non linear dissipative term by vitillaro s argument

global existence and blow up phenomena for a nonlinear wave equation abstract in this paper we study the solution to the initial boundary value problem for a class of nonlinear wave equations with damping and source term by using the energy compensation method we prove that under some conditions on the initial value the growth orders of the nonlinear strain term the damping term and the source term the solution to the problem exists globally and blows up respectively and the estimate for the blow up time is given

two grid mfeas for the incompressible stokes type variational inequality with damping abstract in this paper we study two grid mixed finite element algorithms mfeas for the stationary incompressible stokes equations with damping and nonlinear slip boundary conditions we set up the weak formulation and obtain the well posedness then employing the mixed finite element method some optimal error estimates between the exact solution and the approximation solution are derived two kinds of two grid mfeas based on the stokes correction and newton type correction are established some error estimates for two grid mfeas are obtained several numerical results are presented to confirm our theoretical findings

the existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term abstract in this paper we consider a plate equation with a logarithmic nonlinearity in the presence of a frictional damping we prove for a suitably chosen initial data a global existence as well as a decay result

kirchhoff type system with linear weak damping and logarithmic nonlinearities abstract for the nonlinear kirchhoff type wave system with logarithmic nonlinearities and weak dissipation the global well posedness of initial boundary value problem is analyzed focusing on the interplay between kirchhoff terms and logarithmic sources we investigate the kirchhoff system controlled by logarithmic forces thus amplifying the difficulties in blow up analysis which is the primary scenario of interest by employing potential well method and concavity method we obtain several results related to the sufficient conditions posed on subcritical initial energy and critical initial energy which is used to classify initial data for global existence and finite time blow up finally via careful analysis involving the unstable invariant set under supercritical initial energy we are able to show an affirmative result that the solution blows up in finite time when initial data satisfy some suitable assumptions

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

exponential and polynomial decay for a quasilinear viscoelastic equation abstract we consider the following nonlinear viscoelastic equation u t u t t u u t t 0 t g t s u s d s 0 in a bounded domain for 0 we show that the dissipation induced by the integral term is strong enough to stabilize the solution this result improves an earlier one given by cavalcanti et al in m m cavalcanti v n d cavalcanti j ferreira existence and uniform decay for nonlinear viscoelastic equation with strong damping math methods appl sci 24 2001 1043 1053

global nonexistence of positive initial energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms this work is concerned with a system of viscoelastic wave equations with nonlinear damping and source terms acting in both equations we prove a global nonexistence theorem for certain solutions with positive initial energy

blow up in a nonlinear viscoelastic wave equation with strong damping abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u p 2 u in 0 t with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g we show the finite time blow up of some solutions whose initial data have arbitrarily high initial energy

local existence and uniqueness for a semilinear accretive wave equation abstract we study local existence and uniqueness in the phase space h h 1 r n of the solution of the semilinear wave equation u t t u u t u t p 1 for p 1

non existence of weak solutions to nonlinear damped wave equations in exterior domains abstract we consider the initial boundary value problem of the nonlinear damped wave equation in an exterior domain t 2 u u t u u p t 0 x u 0 x u 0 x t u 0 x u 1 x x u 0 t 0 x when 1 p 1 2 n and the initial data u 0 u 1 h 0 1 l 2 having compact support we prove the non existence of non negative global solutions of the above problem we employ the kaplan fujita h fujita on the blowing up of solutions of the cauchy problem for u t u u 1 j sci univ tokyo sec i 13 1966 109 124 s kaplan on the growth of solutions quasi linear parabolic equations comm pure appl math 16 1963 305 330 method to avoid the difficulty of the reflection from the boundary

blow up for semilinear wave equation with boundary damping and source terms abstract in this paper we consider the semilinear wave equation with boundary damping and source terms this work is devoted to prove a finite time blow up result under suitable condition on the initial data and positive initial energy

phased burst error correcting array codes various aspects of single phased burst error correcting array codes are explored these codes are composed of two dimensional arrays with row and column parities with a diagonally cyclic readout order they are capable of correcting a single burst error along one diagonal optimal codeword sizes are found to have dimensions n sub 1 n sub 2 such that n sub 2 is the smallest prime number larger than n sub 1 these codes are capable of reaching the singleton bound a new type of error approximate errors is defined in q ary applications these errors cause data to be slightly corrupted and therefore still close to the true data level phased burst array codes can be tailored to correct these codes with even higher rates than before

blow up and boundedness for high energies of a quasilinear riser equation abstract we consider a quasilinear wave equation of fourth order that models the mechanical vibrations of a marine riser we study qualitative properties such as boundedness and blow up of solutions with respect to the norm of some hilbert space h for any real value of the initial energy to this end we use invariant sets

stabilized low order finite elements for stokes equations with damping abstract in this paper we consider the stationary stokes equations with damping low order mixed finite element spaces are used to approximate the velocity and the pressure and a local pressure projection stabilization method is used for the pairs to overcome the lack of the inf sup condition the stability of this method is proved and the optimal order error estimates are derived by some nonlinear analysis techniques at last two numerical examples are implemented to test the stability and effectiveness of the proposed method

global existence and blow up of solutions for a system of nonlinear viscoelastic wave equations with damping and source abstract in this paper we investigate the global existence and finite time blow up of solutions to the system of nonlinear viscoelastic wave equations u t t u 0 t g 1 t u d u t m 1 u t f 1 u v v t t v 0 t g 2 t v d v t r 1 v t f 2 u v in 0 t with initial and dirichlet boundary conditions where is a bounded domain in r n n 1 2 3 under suitable assumptions on the functions g i f i i 1 2 the initial data and the parameters in the equations we establish several results concerning local existence global existence uniqueness and finite time blow up property

global existence uniform decay and blow up of solutions for a system of petrovsky equations abstract in this paper we investigate global existence uniform decay and blow up of solutions for the following petrovsky equations u t t 2 u u t p 1 u t f u u v x t 0 t v t t 2 v v t q 1 v t f v u v x t 0 t where is a bounded domain of r n n 1 2 3 having a smooth boundary and f is a c 1 function given by f u v u v r 1 2 u v r 1 2 r 3 1 0 for the case of p q 1 we obtain the blow up of solutions and the lifespan estimates for four different ranges of initial energy for the case of 1 p q r we show the blow up of solutions when the initial energy is negative or nonnegative at less than the mountain pass level value global existence of solutions is proved by the potential well theory and decay estimates of the energy function are established by using nakao s inequality

blow up for solutions of some linear wave equations with mixed nonlinear boundary conditions this paper deals with the blow up in solutions of some linear wave equations with mixed nonlinear boundary conditions the finite time blow up in solutions are caused from the nonlinear boundary conditions even if the initial data are smooth and well defined for all times the pointwise blow up in exact solution and blow up in energy solution are investigated

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