large time behavior of solutions for a system of nonlinear damped wave equations abstract we consider the cauchy problem of the semilinear damped wave system t 2 u u t u f u t 0 x r n u j 0 x a j x t u j 0 x b j x x r n where u t x u 1 t x u m t x with m 2 and j 1 m we show the asymptotic behavior of solutions under the sharp condition on the nonlinear exponents which is a natural extension of the results for the single nonlinear damped wave equations nishihara 2003 21 hayashi et al 2004 9 hosono and ogawa 2004 10 the proof is based on the l p l q type decomposition of the fundamental solutions of the linear damped wave equations into the dissipative part and hyperbolic part hosono and ogawa 2004 10 nishihara 2003 21

existence and non existence of global solutions of the cauchy problem for higher order semilinear pseudo hyperbolic equations abstract we consider the cauchy problem for a higher order pseudo hyperbolic equation using the l p l q type estimation for the corresponding linear problem the existence and non existence criteria of global solutions are found the existence and uniqueness of smooth global solutions are also investigated we also establish the behavior of solutions and their derivatives as t

a problem with the likelihood ratio test for a change point hazard rate model summary a likelihood ratio test for constant hazard against a step change alternative has received considerable attention in recent years additional information in the maximum likelihood estimate of the change point can seriously affect interpretation of test results some simple modifications are considered for which exact percentage points can be derived monte carlo power and mean squared error comparisons are encouraging

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

estimation in change point hazard rate models summary this paper discusses the estimation of parameters in hazard rate models with a changepoint due to the irregularity of the models the classical maximum likelihood method and the method of moments cannot be used a consistent estimator of the change point is obtained by examining the properties of the density represented as a mixture the performance of the estimator is checked via simulation

global existence of small data solutions for wave models with super exponential propagation speed abstract we consider semi linear classical damped wave models with time dependent speed of propagation and time dependent dissipation the right hand side is a power nonlinearity which can be interpreted only as a source term we are interested in the interplay of time dependent coefficients on the global existence of small data solutions the considerations are divided into two cases depending on the behavior of the propagation speed the super exponential and the sub exponential case in this paper we study the super exponential case one main tool of our approach is the use of matsumura type estimates for a family of cauchy problems depending on a parameter

critical exponents for semilinear dissipative wave equations in rn abstract we shall present new critical exponents 1 2m n with m 1 2 to the cauchy problem utt u ut u p 1u with the initial data u 0 u 1 h 1 r n l m r n l 2 r n l m r n that is the small data global existence property can be derived to the cauchy problem above with power 1 2m n

multiplicity of positive solutions for a singular and critical problem abstract in this paper we study the following singular critical elliptic problem p u u u q u in u 0 u 0 in where r n n 3 is a bounded domain with smooth boundary 0 0 1 q 2 1 n 2 n 2 and a smooth function with subcritical asymptotic behaviour at we show the existence of multiple positive solutions of the problem p by combining variational and sub super solution methods

brezis nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem abstract we study brezis nirenberg type theorems for the equation u g x u f x u in u 0 on where is a bounded domain in r n g x is increasing and f is a dissipative nonlinearity we apply such theorems for studying existence and multiplicity of positive solutions for the equation u u q u p in u 0 on where q 0 p 1 and 0

global existence nonexistence and asymptotic behavior of solutions for the cauchy problem of semilinear heat equations abstract in this paper we study the cauchy problem of semilinear heat equations by introducing a family of potential wells we first prove the invariance of some sets and isolating solutions then we obtain a threshold result for the global existence and nonexistence of solutions finally we discuss the asymptotic behavior of the solution

optimal decay rate of solutions for cahn hilliard equation with inertial term in multi dimensions abstract the cauchy problem of the cahn hilliard equation with inertial term is considered based on green s function method together with energy estimates we get the global in time existence and optimal decay rate of solutions furthermore the viscous case is investigated in the last section

confidence regions and tests for a change point in a sequence of exponential family random variables summary maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables with particular emphasis on the exponential distribution the exact null and alternative distributions of the test statistics are found and the power is compared with a test based on a linear trend statistic exact and approximate confidence regions for the change point are based on the values accepted by a level x likelihood ratio test and a modification of the method proposed by cox spj0tvoll 1982 the methods are applied to a classical data set on the time intervals between coal mine explosions and the change in variation of stock market returns in both cases the confidence regions for the change point cover historical events that may have caused the changes

existence and nonexistence of global solutions for a class of nonlinear wave equations of higher order abstract in this paper we investigate the existence and uniqueness of the solution to the cauchy problem for a class of nonlinear wave equations of higher order and prove the existence and nonexistence of global solutions to this problem by a potential well method

explosive solutions of stochastic wave equations with damping on r d a class of strong damped stochastic wave equations driven by multiplicative noises is considered in this article by using an appropriate energy inequality we shall give sufficient conditions such that the local solutions of the stochastic equations are blowup with positive probability or explosive in l2 sense

inference for a hazard rate change point summary we discuss inference based on the likelihood ratio process for a hazard rate change point a random change of time scale transforms the empirical process into a poisson process which enables us to derive large deviation approximations to the significance level of the likelihood ratio test we derive approximate confidence regions for the change point and joint confidence regions for the change point and size of change the effect of censorship is also discussed the methods are illustrated using stanford heart transplant data for which the 70 days following the transplant are found to be most critical

asymptotic behaviors of solutions for viscoelastic wave equation with space time dependent damping term abstract in this paper we consider a viscoelastic wave equation with an absorbing term and space time dependent damping term based on the weighted energy method and by assuming that the kernel decaying exponentially we obtain the l 2 decay rates of the solutions more precisely we show that the decay rates are the same as those obtained in lin et al 2010 15 for the semilinear wave equation with absorption term

a blow up result for a nonlinear damped wave equation in exterior domain the critical case abstract we consider the initial boundary value problem of the nonlinear damped wave equation in an exterior domain we prove a blow up result which generalizes the result of non existence of global solutions of ogawa and takeda 2009 we also show that the critical exponent belongs to the blow up case

on some critical problems for the fractional laplacian operator abstract we study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional laplacian 2 u u q u n n u 0 in u 0 on where r n is a smooth bounded domain n 1 0 0 q n n 0 min n 2 for suitable conditions on depending on q we prove in the case q 1 there exist at least two solutions for every 0 and some 0 at least one if no solution if for q 1 we show existence of at least one solution for 0 1 and nonexistence for 1 when q 1 the existence is shown for every 0 also we prove that the solutions are bounded and regular

exact percentage points of the likelihood ratio test for a change point hazard rate model we wish to test that the hazard rate of survival or failure time data is constant against the alternative of a change in hazard after an unspecified time the likelihood ratio is unbounded but the exact null distribution of a restricted likelihood ratio test statistic is found this distribution is not affected by type ii censoring but it does depend very strongly on the interval in which the unknown change point is assumed to lie some exact percentage points are given which are much larger than simulated points that have been reported in the literature

multiple positive solutions for kirchhoff type of problems with singularity and critical exponents abstract in this paper we study multiplicity of positive solutions for a class of kirchhoff type of equations with the nonlinearity containing both singularity and critical exponents we obtain two positive solutions via the variational and perturbation methods

the brezis nirenberg result for the fractional laplacian the aim of this paper is to deal with the non local fractional counterpart of the laplace equation involving critical non linearities studied in the famous paper of brezis and nirenberg 1983 namely our model is the equation su u u 2 2u in u 0 in rn where s is the fractional laplace operator s 0 1 is an open bounded set of rn n 2s with lipschitz boundary 0 is a real parameter and 2 2n n 2s is a fractional critical sobolev exponent in this paper we first study the problem in a general framework indeed we consider the equation lku u u 2 2u f x u 0 in u 0 in rn where lk is a general non local integrodifferential operator of order s and f is a lower order perturbation of the critical power u 2 2u in this setting we prove an existence result through variational techniques then as a concrete example we derive a brezis nirenberg type result for our model equation that is we show that if 1 s is the first eigenvalue of the non local operator s with homogeneous dirichlet boundary datum then for any 0 1 s there exists a non trivial solution of the above model equation provided n 4s in this sense the present work may be seen as the extension of the classical brezis nirenberg result to the case of non local fractional operators

on space time means and strong global solutions of nonlinear hyperbolic equations on demontre l existence de solutions globales appartenant a l loc r 2 l 2 2 r n pour des equations non lineaires de la forme t u u b x d u f u 0 t x r r n u 0 x 0 x t u 0 x 1 x x r n

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

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

decay estimates for the damped wave equation with weighted odd initial data abstract in this paper we consider the cauchy problem to the damped wave equation several authors have shown the diffusive structure of the problem which has been represented by l p l q estimates we show the new l p l q estimates to the problem when initial data are odd and belong to certain weighted function space these l p l q estimates imply the new decay estimates for the above cauchy problem moreover we apply the above decay estimates to the cauchy problem for the semilinear wave equation with power nonlinearities lower than fujita critical exponent we show the existence of the time global solutions when the initial data are small and odd

existence non existence and asymptotic behavior of global solutions to the cauchy problem for systems of semilinear hyperbolic equations with damping terms abstract we consider the cauchy problem for systems of semilinear hyperbolic equations using the l p l q type estimation for the corresponding linear parts the existence and uniqueness of weak global solutions are investigated we also established the behavior of solutions and their derivatives as t using the method of test functions developed in the works mitidieri and pokhozhaev 2001 11 veron and pohozaev 2001 12 and caristi 2000 23 we obtain the analogue of the fujita hayakawa type criterion for the absence of global solutions to some system of semilinear hyperbolic inequalities with damping it follows that the conditions of existence theorem imposed on the growth of nonlinear parts are exact in some sense

weakly coupled systems of semilinear effectively damped waves with time dependent coefficient different power nonlinearities and different regularity of the data abstract we study the global existence of small data solutions to the cauchy problem for semilinear damped wave equations with an effective dissipation term where the data are supposed to belong to different classes of regularity we apply these results to the cauchy problem for weakly coupled systems of semilinear effectively damped waves with respect to the defined classes of regularity for different power nonlinearities

stochastic wave equation of pure jumps existence uniqueness and invariant measures abstract in this paper we investigate a class of nonlinear damped stochastic hyperbolic equations with jumps the jump component considered here is described as a poisson point process this paper is divided into two parts the first part deals with existence and uniqueness of global weak and strong solutions to this type of equations based on the energy approach the second part devotes to the existence and support of invariant measures corresponding to the weak solution semi group based on markov property of the solution

asymptotic score statistic processes and tests for constant hazard against a change point alternative the problem of testing for a constant failure rate against alternatives with failure rates involving a single change point is considered the asymptotic significance level for tests based on maximal score statistics are shown to involve the solution to a first passage time problem for an ornstein uhlenbeck process an example illustrates the methodology

central manifold theory for the generalized equation of kirchhoff strings on rn we consider the generalized quasilinear dissipative kirchhoff s string problem utt a 1 2 u 2 au aut f u x r n t 0 withthe initial conditions u x 0 u0 x and ut x 0 u1 x in the case where n 3 0 the purpose of our work is to study the stability of the initial solution u 0 for this equation using central manifold theory

on potential wells and applications to semilinear hyperbolic equations and parabolic equations abstract in this paper we generalize the family of potential wells to the initial boundary value problem of semilinear hyperbolic equations and parabolic equations u tt u f u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 and u t u f u x t 0 u x 0 u 0 x x u x t 0 x t 0 not only give a threshold result of global existence and nonexistence of solutions but also obtain the vacuum isolating of solutions finally we prove the global existence of solutions for above problem with critical initial conditions i u 0 0 e 0 d or i u 0 0 j u 0 d so payne and sattinger s results are generalized and improved in essential

the nehari manifold for fractional kirchhoff problems involving singular and critical terms abstract in the present paper we study the following singular kirchhoff problem m r 2 n u x u y 2 x y n 2 s d x d y s u f x u g x u 2 s 1 in u 0 in u 0 in r n where r n is an open bounded domain dimension n 2 s with s 0 1 2 s 2 n n 2 s is the fractional critical sobolev exponent parameter 0 exponent 0 1 m models a kirchhoff coefficient f l 2 s 2 s 1 is a positive weight while g l is a sign changing function using the idea of nehari manifold technique we prove the existence of at least two positive solutions for a sufficiently small choice of this approach allows us to avoid any restriction on the boundary of

on decay properties of solutions for degenerate strongly damped wave equations of kirchhoff type abstract we consider the initial boundary value problem for the degenerate strongly damped wave equations of kirchhoff type u a 1 2 u x t 2 d x a u a u 0 for all t 0 we will give the optimal decay estimate c 1 1 t 1 a 1 2 u t 2 c 1 t 1 when either the coefficient is appropriately small or the initial data are appropriately small and we will show a decay property of the norm a u t 2 for t 0

cauchy problem for a class of nonlinear dispersive wave equations arising in elasto plastic flow abstract the paper studies the existence both locally and globally in time stability decay estimates and blowup of solutions to the cauchy problem for a class of nonlinear dispersive wave equations arising in elasto plastic flow under the assumption that the nonlinear term of the equations is of polynomial growth order say it proves that when 1 the cauchy problem admits a unique local solution which is stable and can be continued to a global solution under rather mild conditions when 5 and the initial data is small enough the cauchy problem admits a unique global solution and its norm in l 1 p r decays at the rate 1 t p 2 2 p for 2 p 10 and if the initial energy is negative then under a suitable condition on the nonlinear term the local solutions of the cauchy problem blow up in finite time

on family of potential wells and applications to semilinear hyperbolic equations and parabolic equations abstract we study the initial boundary value problem for semilinear hyperbolic equations and parabolic equations with convex function nonlinear terms by introducing a family of potential wells we not only obtain the invariant sets and vacuum isolation of solutions but also give a threshold result of global existence and nonexistence of solutions moreover we discuss the global existence of solution for problem with critical initial condition e 0 d or j u 0 d which fills some important gaps regarding this problem finally we prove the global nonexistence of solution and asymptotic behavior of solution for semilinear parabolic equations

best constants for sobolev inequalities for higher order fractional derivatives we obtain sharp constants for sobolev inequalities for higher order fractional derivatives as an application we give a new proof of a theorem of w beckner concerning conformally invariant higher order differential operators on the sphere

the pointwise estimates of solutions for semilinear dissipative wave equation in multi dimensions abstract in this paper we study the global in time existence and the pointwise estimates of solutions to the cauchy problem for the dissipative wave equation in multi dimensions using the fixed point theorem we obtain the global existence of the solution in addition the pointwise estimates of the solution are obtained by the method of the green function furthermore we obtain the l p 1 p convergence rate of the solution

global existence and asymptotic behavior of solutions for a semi linear wave equation abstract in this paper we investigate the initial value problem for a semi linear wave equation in n dimensional space based on the decay estimate of solutions to the corresponding linear equation we define a set of time weighted sobolev spaces under small condition on the initial value we prove the global existence and asymptotic behavior of the solution in the corresponding sobolev spaces by the contraction mapping principle

global existence of small amplitude solutions to nonlinear klein gordon equations in four space time dimensions consider the following class of nonlinear wave equations square text u u text text f u u u n k g where t 2 1 2 2 2 3 2 is the d alembertian of the 4 dimensional minkowski space time and f a smooth function of u u t x and its first and second partial derivates vanishing together with its first derivatives at u u u 0 in other words f is at least quadratic in u u u in a neighborhood of the trivial solution u 0 we subject u to the pure initial value problem text u mkern 1mu varepsilon text f x u t varepsilon g x at t 0 i v p with f g c 0 3 and e 0 a small parameter

fourth order wave equations with nonlinear strain and source terms abstract in this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms first we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions then we obtain a threshold result of global existence and nonexistence finally we discuss the global existence of solutions for the problem with critical initial condition i u 0 0 e 0 d so the esquivel avila s results are generalized and improved

global existence and optimal time decay estimates of solutions to the generalized double dispersion equation on the framework of besov spaces abstract we investigate the initial value problem for the generalized double dispersion equation in any dimensions inspired by 28 for the hyperbolic system of first order pdes we develop littlewood paley pointwise energy estimates for the dissipative wave equation of high order furthermore with aid of the frequency localization duhamel principle we establish the global existence and optimal decay estimates of solutions in spatially critical besov spaces our results could hold true for any dimensions n 1 indeed the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks

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

decay estimates for dissipative wave equations in exterior domains abstract we study the exterior initial boundary value problem for the linear dissipative wave equation t u 0 in 0 with u t u t 0 u 0 u 1 and u 0 where is an exterior domain in n dimensional euclidean space r n we first show higher local energy decay estimates of the solution u t and then using the cut off technique together with those estimates we can obtain the l 1 estimate of the solution u t when n 3 that is u t l 1 c u 0 h n u 1 h n 1 u 0 w n 1 u 1 w n 1 1 for t 0 where n n 2 is the integer part of n 2 moreover by induction argument we derive the higher energy decay estimates of the solution u t for t 0

large time behavior and lp lq estimate of solutions of 2 dimensional nonlinear damped wave equations abstract we show the asymptotic behavior of the solution to the cauchy problem of the two dimensional damped wave equation it is shown that the solution of the linear damped wave equation asymptotically decompose into a solution of the heat and wave equations and the difference of those solutions satisfies the lp lq type estimate this is a two dimensional generalization of the three dimensional result due to nishihara math z 244 2003 631 to show this we use the fourier transform and observe that the evolution operators of the damped wave equation can be approximated by the solutions of the heat and wave equations by using the lp lq estimate we also discuss the asymptotic behavior of the semilinear problem of the damped wave equation with the power nonlinearity u u our result covers the whole super critical case 1 where the 1 is well known as the fujita exponent when n 2

potential well method for cauchy problem of generalized double dispersion equations abstract in this paper we study cauchy problem of generalized double dispersion equations u t t u x x u x x t t u x x x x f u x x where f u u p p 1 or u 2 k k 1 2 by introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions but also obtain the invariance of some sets and vacuum isolating of solutions in addition the global existence and finite time blow up of solutions for problem with critical initial conditions e 0 d i u 0 0 or i u 0 0 are proved

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

existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping abstract this paper concerns with the cauchy problem for the damped nonlinear hyperbolic system u t t u u t v p t x r 1 r n v t t v v t u q t x r 1 r n u 0 x u 0 x u t 0 x u 1 x x r n v 0 x v 0 x v t 0 x v 1 x x r n where p q 1 and satisfy p q 1 we shall prove that if max 1 p p q 1 1 q p q 1 n 2 for n 1 or 3 then the solution with small initial data exists globally in time and satisfies the decay estimates u t c 1 t and v t c 1 t for some positive constants and while if max 1 p p q 1 1 q p q 1 n 2 for n 1 then every solution with initial data having positive average value does not exist globally

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

conservative finite difference scheme for the nonlinear fourth order wave equation abstract a conservative finite difference scheme is presented for solving the two dimensional fourth order nonlinear wave equation the existence of the numerical solution of the finite difference scheme is proved by brouwer fixed point theorem with the aid of the fact that the discrete energy is conserved the finite difference solution is proved to be bounded in the discrete l norm then the difference solution is shown to be second order convergent in the discrete l norm a numerical example shows the efficiency of the proposed scheme

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

global solution for a generalized boussinesq equation this paper considers the existence and uniqueness of the solution to the cauchy problem for a class of boussinesq equation proves the global existence and finite time blowup of the solution to the problem by the potential well method

global existence and nonexistence of solutions for a system of nonlinear damped wave equations abstract we consider the cauchy problem for the system of semilinear damped wave equations with small initial data t 2 u 1 u 1 t u 1 u k p 1 t 0 x r n t 2 u 2 u 2 t u 2 u 1 p 2 t 0 x r n t 2 u k u k t u k u k 1 p k t 0 x r n u j 0 x a j x t u j 0 x b j x x r n 1 j k we show that a critical exponent which classifies the global existence and the finite time blow up of solutions indeed coincides with the one to a corresponding semilinear heat systems with small data the proof of the global existence is based on the l p l q estimates of fundamental solutions for linear damped wave equations k nishihara l p l q estimates of solutions to the damped wave equation in 3 dimensional space and their application math z 244 2003 631 649 k marcati p nishihara the l p l q estimates of solutions to one dimensional damped wave equations and their application to compressible flow through porous media j differential equations 191 2003 445 469 t hosono t ogawa large time behavior and l p l q estimate of 2 dimensional nonlinear damped wave equations j differential equations 203 2004 82 118 t narazaki l p l q estimates for damped wave equations and their applications to semilinear problem j math soc japan 56 2004 585 626 and the blow up is shown by the fujita kaplan zhang method q zhang a blow up result for a nonlinear wave equation with damping the critical case c r acad sci paris 333 2001 109 114 f sun m wang existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping nonlinear anal 66 12 2007 2889 2910 t ogawa h takeda non existence of weak solutions to nonlinear damped wave equations in exterior domains nonlinear anal 70 10 2009 3696 3701

global and blow up solutions for a system of nonlinear hyperbolic equations with dissipative terms abstract in this paper we study a nonlinear hyperbolic system with strong damping firstly by use of the successive approximation method and a series of classical estimates we prove the local existence and uniqueness of weak solution secondly via some inequalities applying the potential method and the concave method we discuss the asymptotic and blow up behavior of weak solution with different conditions