Global existence and asymptotic behavior of solutions for a semi-linear wave equation

被引：30

作者：

Wang, Yu-Zhu ^{[1
]}

Liu, Fagui ^{[1
]}

Zhang, Yuanzhang ^{[1
]}

机构：

[1] N China Univ Water Resources & Elect Power, Sch Math & Informat Sci, Zhengzhou 450011, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 385卷 / 02期

关键词：

Semi-linear wave equation; Global existence; Asymptotic behavior; CLASSICAL-SOLUTIONS; CAUCHY-PROBLEM;

D O I：

10.1016/j.jmaa.2011.07.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the initial value problem for a semi-linear wave equation in n-dimensional space. Based on the decay estimate of solutions to the corresponding linear equation, we define a set of time-weighted Sobolev spaces. Under small condition on the initial value, we prove the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces by the contraction mapping principle. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：836 / 853

页数：18

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