Nonlinear wave equations on the two-dimensional sphere
type: Item
instance of: scholarly article
title: Nonlinear wave equations on the two-dimensional sphere
zbMATH Open document ID: 1006.35069
author: Mohammad Rammaha
author: Theresa A. Strei
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-02T00:00:00Z
review text: This paper is devoted to an initial value problem on the two-dimensional sphere \(S^2\), that is \[ \begin{cases} u_{tt}-\Delta u=G(u),\\ u(x,0)=u_0,\;u_t(x,0)= u_1,\end{cases}\tag{1} \] where \(\Delta\) is the Laplace-Beltrami operator on \(S^2\). Under some suitable assumptions on \(G(u)\) the authors prove existence and uniqueness of a local regular solution. Morevoer they show that a large class of solutions to the initial value problem quench in finite time.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 58J45
zbMATH DE Number: 1749659
zbMATH Keywords: quenching in finite time
zbMATH Keywords: Laplace-Beltrami operator
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2088401093
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DOI: 10.1006/JMAA.2000.6722
description: scientific article; zbMATH DE number 1749659