@Article{JPDE-36-235,
author = {Guo , FeiLiang , Jinling and Xiao , Changwang},
title = {Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping},
journal = {Journal of Partial Differential Equations},
year = {2023},
volume = {36},
number = {3},
pages = {235--261},
abstract = {<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>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v36.n3.1},
url = {http://global-sci.org/intro/article_detail/jpde/21887.html}
}