Global existence of solutions for semilinear damped wave equations in RN with noncompactly supported initial data

被引：122

作者：

Ikehata, R ^{[1
]}

Tanizawa, K ^{[1
]}

机构：

[1] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 61卷 / 07期

关键词：

semilinear damped wave equation; N-D Cauchy problem; noncompactly supported initial data; small energy; critical exponent; global existence;

D O I：

10.1016/j.na.2005.01.097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the N-dimensional Cauchy problem in R-N for a semilinear damped wave equation with a power-type nonlinearity vertical bar u vertical bar(p). For a noncompactly supported initial data, which has a small energy, we shall derive a global in time existence result in the case when the power of the nonlinear term satisfies 1 + 2/N < p <= N/[N - 2](+). This generalizes a previous result due to Todorova-Yordanov (J. Differential Equations 174 (2001) 464-489), which dealt with a solution in the framework of compactly supported initial data. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：1189 / 1208

页数：20

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