The Cauchy problem for the nonlinear damped wave equation with slowly decaying data

被引：20

作者：

Ikeda, Masahiro ^{[1
]}

Inui, Takahisa ^{[1
]}

Wakasugi, Yuta ^{[2
]}

机构：

[1] Kyoto Univ, Dept Math, Grad Sch Sci, Kyoto 6068502, Japan

[2] Ehime Univ, Grad Sch Sci & Engn, Dept Engn Prod & Environm, Matsuyama, Ehime 7908577, Japan

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2017年 / 24卷 / 02期

基金：

日本学术振兴会;

关键词：

Nonlinear damped wave equation; Slowly decaying data; Global well-posedness; Asymptotic behavior; Blow-up; Estimates of lifespan; LARGE TIME BEHAVIOR; DIFFUSION PHENOMENON; ASYMPTOTIC-BEHAVIOR; GLOBAL EXISTENCE; CRITICAL EXPONENT; LIFE-SPAN; R-N; SYSTEM; NONEXISTENCE; PROFILES;

D O I：

10.1007/s00030-017-0434-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Cauchy problem for the nonlinear damped wave equation and establish the large data local well-posedness and small data global well-posedness with slowly decaying initial data. We also prove that the asymptotic profile of the global solution is given by a solution of the corresponding parabolic problem, which shows that the solution of the damped wave equation has the diffusion phenomena. Moreover, we show blow-up of solution and give the estimate of the lifespan for a subcritical nonlinearity. In particular, we determine the critical exponent for any space dimension.

引用

页数：53

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