Global existence, blow-up and asymptotic behavior of solutions for a class of coupled nonlinear Klein-Gordon equations with damping terms
type: Item
instance of: scholarly article
title: Global existence, blow-up and asymptotic behavior of solutions for a class of coupled nonlinear Klein-Gordon equations with damping terms
zbMATH Open document ID: 1259.35134
author: Shun-Tang Wu
published in: Acta Applicandae Mathematicae
publication date: 2012-12-27T00:00:00Z
review text: The author investigates the global existence, asymptotic behavior and blow-up of the solutions of the initial value problem to the coupled equations \[ \begin{cases} u_{tt}-\Delta u+m_1^2u+\gamma _1u_t=(| u| ^{2p}+| v| ^{p+1}| u| ^{p-1})u,\\ v_{tt}-\Delta v+m_2^2v+\gamma _2v_t=(| v| ^{2p}+| u| ^{p+1}| v| ^{p-1})v \end{cases} \] for \(t>0\), \(x\in \mathbb{R}^n\), where \(n\geq 2\), \(m_1,m_2,\gamma _1,\gamma _2>0\), \(p>0\) for \(n=2\) and \(0<p<2/(n-2)\) for \(n\geq 3\). He introduces the family of potential wells, and with use of that he presents a sharp criterion for global existence or blow-up of the solutions.
Mathematics Subject Classification ID: 35L52
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L71
zbMATH DE Number: 6118576
zbMATH Keywords: potential well
zbMATH Keywords: ground state solution
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: s10440-011-9662-2
OpenAlex ID: W2016501335
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DOI: 10.1007/S10440-011-9662-2
description: scientific article; zbMATH DE number 6118576