EXPONENTIAL DECAY FOR SOLUTIONS TO SEMILINEAR DAMPED WAVE EQUATION

被引：29
|
作者：
Gerbi, Stephane [1 ]
Said-Houari, Belkacem [2 ]
机构：
[1] Univ Savoie, Math Lab, F-73376 Le Bourget Du Lac, France
[2] KAUST, Div Math & Comp Sci & Engn, Thuwal 239556900, Saudi Arabia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2012年 / 5卷 / 03期
关键词：
Strong damping; stable set; global existence; decay rate; positive initial energy; GLOBAL-SOLUTIONS; NONEXISTENCE THEOREMS; EVOLUTION-EQUATIONS; CAUCHY-PROBLEM; BLOW-UP; EXISTENCE; INSTABILITY;
D O I：
10.3934/dcdss.2012.5.559
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].
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页码：559 / 566
页数：8
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