Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping

被引：0
|
作者：
Fei, Guo [1 ,2 ]
Jinling, Liang [1 ]
Changwang, Xiao [3 ]
机构：
[1] Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Peoples R China
[2] Nanjing Normal Univ, Jiangsu Key Lab NSLSCS, Nanjing 210023, Peoples R China
[3] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
来源：
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 36卷 / 03期
关键词：
Key Words; Semilinear wave equation; time-dependent damping; life-span; global iteration meth-od; BLOW-UP; CRITICAL EXPONENT; CAUCHY-PROBLEM; DISSIPATION;
D O I：
10.4208/jpde.v36.n3.1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the Cauchy problem for a semilinear wave equation with a time-dependent damping. In case that the space dimension n =1 and the nonlinear power is bigger than 2, the life-span Te(& epsilon;) and global existence of the classical solution to the problem has been investigated in a unified way. More precisely, with respect to different values of an index K, which depends on the time-dependent damping and the nonlinear term, the life-span Te(& epsilon;) can be estimated below by & epsilon; - p 1-K , e & epsilon;-p or +& INFIN;, where & epsilon; is the scale of the compact support of the initial data.
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页码：235 / 261
页数：27
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