Lifespan Estimates for a Class of Semilinear Wave Equations with Time- and Space-Dependent Coefficients on the Power Nonlinearity

被引:0
作者
Yuanfei Li
机构
[1] Guangzhou Huashang College,School of Data Sciences
来源
Mediterranean Journal of Mathematics | 2023年 / 20卷
关键词
Semilinear wave equation; lifespan estimate; variable coefficient; blow-up; Primary 35L71; Secondary 35B44; 35B33;
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摘要
In the present paper, we are interested in the blow-up condition and upper bound estimates of lifespan for a class of semilinear wave equations with power nonlinearity in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^n$$\end{document}, which includes time- and space-dependent coefficients. With the use of an iteration procedure and some time-dependent functionals, we derive blow-up results for all dimensional cases. Particularly, optimal result in one-dimensional case and a threshold to distinguish different blow-up behaviors for the range of power exponent in two-dimensional case are obtained. Finally, we give some remarks to behaviors for lifespan estimates.
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