Existence and Asymptotic Behavior of Solutions to Semilinear Wave Equations with Nonlinear Damping and Dynamical Boundary Condition

被引：6

作者：

Yassine, Hassan ^{[1
,2
]}

机构：

[1] Univ Lorraine, Lab Math & Applicat Metz, F-57045 Metz 1, France

[2] CNRS, UMR 7122, F-57045 Metz 1, France

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2012年 / 24卷 / 03期

关键词：

Asymptotic behavior of solutions; Lyapunov function; Stabilization; Dynamical boundary condition; Lojasiewicz-Simon inequality; ANALYTIC NONLINEARITY; CRITICAL EXPONENT; CONVERGENCE; DISSIPATION; EQUILIBRIUM; DECAY;

D O I：

10.1007/s10884-012-9258-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim in this article is to study a nonautonomous semilinear wave equation with nonlinear damping and dynamical boundary condition. First we prove the existence and uniqueness of global bounded solutions having relatively compact range in the natural energy space. Then, by deriving an appropriate Lyapunov energy, we show that if the exponent in the Aojasiewicz-Simon inequality is large enough (depending on the damping), then weak solutions converge to equilibrium.

引用

页码：645 / 661

页数：17

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