Global existence of solutions for a weakly coupled system of semilinear damped wave equations

被引：16

作者：

Nishihara, Kenji ^{[1
]}

Wakasugi, Yuta ^{[2
]}

机构：

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

[2] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 08期

基金：

日本学术振兴会;

关键词：

Semilinear damped wave equation; Weakly coupled system; Global existence; Critical exponent; Lifespan; DIFFUSION PHENOMENON; CAUCHY-PROBLEM; BLOW-UP; CRITICAL EXPONENTS; R-N; TIME; NONEXISTENCE; PROFILES; BEHAVIOR; SPACE;

D O I：

10.1016/j.jde.2015.05.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the Cauchy problem for a weakly coupled system of semilinear damped wave equations. We prove the global existence of solutions for small data in the supercritical case for any space dimension. We also give estimates of the weighted energy of solutions and in a special case, we prove an almost optimal estimate. Moreover, in the subcritical case, we give an almost optimal estimate of the lifespan from both above and below. (C) 2015 Elsevier Inc. All rights reserved.

引用

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页码：4172 / 4201

页数：30

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