Orbital stability of standing waves for semilinear wave equations with indefinite energy
type: Item
instance of: scholarly article
title: Orbital stability of standing waves for semilinear wave equations with indefinite energy
zbMATH Open document ID: 1151.35058
author: Baisheng Yan
author: Zhengfang Zhou
author: Xin-Ming Zhao
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-06-17T00:00:00Z
review text: The paper deals with the orbital stability of standing waves for the nonlinear Klein-Gordon equation \(u_{tt}-\Delta u+m(x)u +g(x,\left| u\right| )u=0\) in \(\mathbb{R}^{+}\times \Omega ,\) where \(\Omega \) denotes \(\mathbb{R}^{n}\) or a bounded domain or a compact manifold. The orbital stability is determined by the convexity of the lowest energy \(d(\omega)\) of the standing waves with the frequency \(\omega .\) The arguments rely on the conservation of energy and charge and the construction of suitable invariant manifolds of solution flows. Existence of standing waves for some special equations, e.g. the case \(m(x)\equiv 1, g=\left| u\right| ^{p-1}\) is obtained as the applications of the results.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 5289203
zbMATH Keywords: nonlinear Klein-Gordon equation
zbMATH Keywords: indefinite energy
zbMATH Keywords: standing wave
zbMATH Keywords: orbital stability
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.03.056
OpenAlex ID: W2112219849
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DOI: 10.1016/J.JMAA.2008.03.056
description: scientific article; zbMATH DE number 5289203