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

作　　者：GUO Fei LIANG Jinling XIAO Changwang 

机构地区：[1]School of Mathematical Sciences and Jiangsu Key Laboratory for NSLSCS,Nanjing Normal University,Nanjing 210023,China [2]School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China [3]Department of Mathematics,Huzhou University,Huzhou 313000,China

出　　处：《Journal of Partial Differential Equations》2023年第3期235-261,共27页偏微分方程（英文版）

基　　金：supported by the NSF of China(11731007);the Priority Academic Program Development of Jiangsu Higher Education Institutions,and the NSF of Jiangsu Province(BK20181381,BK20221320).

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 T(ε)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 T(ε)can be estimated below byε-p/1-k,e^(ε)-p or+∞,where e is the scale of the compact support of the initial data.

关 键 词：Semilinear wave equation time-dependent damping life-span global iteration method. 

分 类 号：O175.27[理学—数学] O175.29[理学—基础数学]