The energy decay and asymptotics for a class of semilinear wave equations in two space dimensions

被引：13

作者：

Katayama, Soichiro ^{[1
]}

Murotani, Daisuke ^{[2
]}

Sunagawa, Hideaki ^{[2
]}

机构：

[1] Wakayama Univ, Dept Math, Wakayama 6408510, Japan

[2] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2012年 / 12卷 / 04期

关键词：

GLOBAL EXISTENCE; LIFE-SPAN; SYSTEMS; BEHAVIOR;

D O I：

10.1007/s00028-012-0160-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions and give an asymptotic description of the solution as t -> infinity uniformly in x is an element of R-2. In particular, our result implies the decay of the energy when the nonlinearity is dissipative.

引用

页码：891 / 916

页数：26

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