Year: 2023
Author: Fei Guo, Jinling Liang, Changwang Xiao
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 3 : pp. 235–261
Abstract
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 $\widetilde T(\varepsilon)$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n3.1
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 3 : pp. 235–261
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Semilinear wave equation time-dependent damping life-span global iteration method.