TY - JOUR
T1 - Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping
AU - Guo , Fei
AU - Liang , Jinling
AU - Xiao , Changwang
JO - Journal of Partial Differential Equations
VL - 3
SP - 235
EP - 261
PY - 2023
DA - 2023/08
SN - 36
DO - http://doi.org/10.4208/jpde.v36.n3.1
UR - https://global-sci.org/intro/article_detail/jpde/21887.html
KW - Semilinear wave equation, time-dependent damping, life-span, global iteration method.
AB - <p style="text-align: justify;">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 $\widetilde T(\varepsilon)$ 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 $\widetilde T(\varepsilon)$&nbsp; can be estimated below by $\varepsilon^{-\frac{p}{1-K}}$, $e^{\varepsilon^{-p}}$ or $+\infty$, where $\varepsilon$ is the scale of the compact support of the initial data.<br/></p>