[PDF] Top 20 Global solutions for a nonlinear hyperbolic equation with boundary memory source term

... coupled in the first equation. Motivated by the above works, we are devoted to study problem (1.1). By virtue of the potential well method, and through Galerkin procedures, we acquire the global existence ... See full document

... obtained global existence results under the growth assumptions on the nonlinear terms and initial ...These global existence results have been improved by Liu and Zhao 16 by using a new ...of ... See full document

... obtain global existence, the authors of [1] used the Galerkin ap- proximation method and the monotonicity method (see ...weak solutions to a class of nonlinear beam equation are established ... See full document

... Global solutions of the Cauc]ly problem for a nonlinear hyperbolic equation, Universit di Pisa, Dipartamento di Matematica, Roma 1982... Local solutions for Nonlinear Anal.[r] ... See full document

... and source term acting in the domain or on the ...single equation, we can cite Cavalcanti et ...of solutions in the domain we can cite the work of Vitillaro [16] and Georgiev and Todorova ... See full document

... the global existence, blow-up so- lutions, and asymptotic properties of the initial boundary value problems for semilin- ear parabolic equations and systems with or without memory ...the ... See full document

... or nonlinear boundary feed- back was investigated by several authors; see, for example, [–] among ...with memory was studied in [–] and the references ...the memory term act- ing in ... See full document

... Wang [42] considered problem (1.1)-(1.2) but with a linear damping (m = 2). They proved the local existence, global existence and finite time blow-up of solutions as well as the estimation on the potential ... See full document

... and source term by using Concavity ...a nonlinear damping ...the nonlinear case (p > 1). They showed that solutions with negative initial energy blow up in finite ...the ... See full document

... the blow-up time if blow-up occurs, or else t ∗ = ∞. It is well known that the functions f and g may greatly affect the behavior of the solution u(x, t) with the development of time. From the physical standpoint, −f is ... See full document

... is global with energy which decays exponentially under the potential ...for solutions starting in the unstable set is proved, but also under some appropriate assumptions on g and the initial data, a blow-up ... See full document

... the boundary condition in (.) is nonlinear but it can be linearized and this makes it possible to establish existence results for posi- tive solutions of ... See full document

... the nonlinear terms considered in our paper are more general, we aim to provide some new results in this ...the global existence and blow up of solutions for the sub-critical case E() < d, where ... See full document

... In this paper, we study the blow-up singularity of a semilinear parabolic equation with nonlinear memory both in the reaction term and the boundary condition. We firstly establish the ... See full document

... was considered. He studied the asymptotic behavior of solutions and found the influence of the weight function on the existence of global and blow-up solutions. Later, Akila [] adopted the method of ... See full document

... of global solutions for nonlinear wave equations with nonlinear damping and source terms [4, 5, 10, 13, 18] in the past twenty ...a global weak solution for the hyperbolic ... See full document

... subject to the homogeneous Dirichlet boundary condition. By using the comparison prin- ciple and constructing a self-similar lower solution, they obtained sufficient conditions for global existence and ... See full document

... with memory term act- ing in the boundary or in the domain, there are numerous results related to asymptotic behavior of ...strong solutions of wave equation (1.1) with a ... See full document

... weak solutions. Furthermore, we show that there are solutions under some conditions on initial data which blow up in finite time with non-positive initial energy as well as positive initial ...of ... See full document

... Local in time existence of positive classical solutions of (1.1) can be obtained by using fixed point theorem [21], the representation formula and the contraction map- ping principle as in [13]. By the above ... See full document