Long time behavior for a semilinear hyperbolic equation with asymptotically vanishing damping term and convex potential

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

May, Ramzi

关键词: Dissipative hyperbolic equation;    Asymptotically small dissipation;    Asymptotic behavior;    Energy function;    Convex function;   

DOI  :  10.1016/j.jmaa.2015.04.067

来源: Elsevier

【 摘 要 】

We investigate the asymptotic behavior, as t goes to infinity, for a semilinear hyperbolic equation with asymptotically small dissipation and convex potential. We prove that if the damping term behaves like K/t(alpha) as t -> +infinity, for some K > 0 and alpha is an element of]0, 1[, then every global solution converges weakly to an equilibrium point. This result is a positive answer to a question left open in the paper of Cabot and Frankel (2012) [6]. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free