Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity

被引：14
|
作者：
Fujiwara, Kazumasa [1 ]
Ikeda, Masahiro [2 ]
Wakasugi, Yuta [3 ]
机构：
[1] Tohoku Univ, Math Inst, Aoba Ku, 6-3 Aoba, Sendai, Miyagi 9808578, Japan
[2] Keio Univ, Fac Sci & Technol, Dept Math, Ctr Adv Intelligence Project,RIKEN,Kohoku Ku, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan
[3] Ehime Univ, Grad Sch Sci & Engn, Dept Engn Prod & Environm, 3 Bunkyo Cho, Matsuyama, Ehime 7908577, Japan
来源：
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2019年 / 62卷 / 02期
基金：
日本学术振兴会;
关键词：
Damped wave equation; Lifespan estimate; Blow-up rate; ASYMPTOTIC PROFILES; SCALING VARIABLES; CRITICAL EXPONENT; GLOBAL-SOLUTIONS; CAUCHY-PROBLEM; LEQUATION; BEHAVIOR;
D O I：
10.1619/fesi.62.157
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study estimates of lifespan and blow-up rates of solutions for the Cauchy problem of the wave equation with a time -dependent damping and a power type non-linearity. When the damping acts on the solutions effectively, and the non linearity belongs to the subcritical case, we show the sharp lifespan estimates and the blow-up rates of solutions. The upper estimates are proved by an ODE argument, and the lower estimates are given by a method of scaling variables.
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页码：157 / 189
页数：33
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