Blow-up solutions of some nonlinear hyperbolic systems
type: Item
instance of: scholarly article
title: Blow-up solutions of some nonlinear hyperbolic systems
zbMATH Open document ID: 0945.35054
author: Keng Deng
published in: Rocky Mountain Journal of Mathematics
publication date: 2000-09-24T00:00:00Z
full work available at URL: CONT29-3.html
review text: The paper deals with initial value problems for two types of systems of two semilinear wave equations \(u_{tt}=\Delta u+|v|^p, v_{tt}=\Delta v+|u|^q,\) and \(u_{tt}=\Delta u+|v_t|^p, v_{tt}=\Delta v+|u_t|^q (t>0, x\in \mathbb{R}^n)\) with compactly supported initial data. The author gives the bound \(B(n,p)\) such, that if \(1<pq<B(n,p),\) all nontrivial solutions of the above problems blow up in finite time.
Mathematics Subject Classification ID: 35L55
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 1439636
zbMATH Keywords: system of two semilinear wave equations
zbMATH Keywords: blow up
zbMATH Keywords: initial value problem
zbMATH Keywords: compactly supported initial data
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
OpenAlex ID: W2061757412
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DOI: 10.1216/RMJM/1181071610
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description: scientific article; zbMATH DE number 1439636