Global nonexistence of solutions to a semilinear wave equation in the Minkowski space

被引：5

作者：

Liu, Xuefei ^{[2
]}

Zhou, Yong ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

[2] Chongqing Three Gorges Univ, Coll Math & Comp Sci, Chongqing 404000, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2008年 / 21卷 / 08期

基金：

中国国家自然科学基金;

关键词：

semilinear wave equation; global nonexistence;

D O I：

10.1016/j.aml.2007.08.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work presents the finite-time blow-up of solutions to the equation u(tt) - Delta u = a(-k) vertical bar u vertical bar(p), in the Minkowski space. We extend the previous result of Belchev, Kepka and Zhou [E. Belchev, M. Kepka, Z. Zhou, Finite-time blow-up of solutions to semilinear wave equations, J. Funct. Anal. 190 (1) (2002) 233-254] comprehensively. Due to a modification of the so-called method of conformal compactification used by Belchev, Kepka and Zhou, we show that the solutions blow up in finite time with more relaxed initial data and extended index p. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：849 / 854

页数：6

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