Critical exponent for the Cauchy problem to the weakly coupled damped wave system

被引：36

作者：

Nishihara, Kenji ^{[1
]}

Wakasugi, Yuta ^{[2
]}

机构：

[1] Waseda Univ, Fac Polit Sci & Econ, Tokyo 1698050, Japan

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 108卷

基金：

日本学术振兴会;

关键词：

Damped wave equation; Weakly coupled system; Critical exponent; Global existence; Lifespan; GLOBAL-SOLUTIONS; BLOW-UP; EXISTENCE; EQUATIONS; NONEXISTENCE; BEHAVIOR;

D O I：

10.1016/j.na.2014.06.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a system of weakly coupled semilinear damped wave equations. We determine the critical exponent for any space dimensions. Our proof of the global existence of solutions for supercritical nonlinearities is based on a weighted energy method, whose multiplier is appropriately modified in the case where one of the exponent of the nonlinear term is less than the so called Fujita's critical exponent. We also give estimates of the lifespan of solutions from above for subcritical nonlinearities. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：249 / 259

页数：11

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