Global existence and blow-up for semilinear wave equations with variable coefficients
type: Item
instance of: scholarly article
title: Global existence and blow-up for semilinear wave equations with variable coefficients
zbMATH Open document ID: 1415.35204
author: Qian Lei
author: Han Yang
published in: Chinese Annals of Mathematics. Series B
publication date: 2018-11-15T00:00:00Z
review text: In this nice paper under review, the authors consider the critical exponent problem for the variable coefficients wave equation with a space dependent potential and source term. For sufficiently small data with compact support, if the power of nonlinearity is larger than the expected exponent, it is proved that there exists a global solution. In addition, the precise decay estimates for the energy, $L^2$ and $L^{p+1}$ norms of solutions are also established. Furthermore, the blow-up of the solutions is also proved for arbitrary initial data with compact support when the power of nonlinearity is less than some constant.
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 6979841
zbMATH Keywords: energy decay
zbMATH Keywords: $L^2$ and $L^{p+1}$ estimates
zbMATH Keywords: initial data with compact support
reviewed by: M. M. Cavalcanti
MaRDI profile type: Publication
full work available at URL: s11401-018-0087-3
OpenAlex ID: W2896765906
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Wikidata QID: Q129089813
DOI: 10.1007/S11401-018-0087-3
description: scientific article; zbMATH DE number 6979841