The global Goursat problem on \(R\times S^ 1\)
type: Item
instance of: scholarly article
title: The global Goursat problem on \(R\times S^ 1\)
zbMATH Open document ID: 0703.35004
DOI: 10.1016/0022-1236(89)90025-6
author: John Baez
author: Zhengfang Zhou
published in: Journal of Functional Analysis
publication date: 1989-01-01T00:00:00Z
review text: The authors study regularity for the Goursat problem for nonlinear wave equation on \(R\times S^ 1\). In the Goursat problem, the data are given on a light cone and lacks the domain dependence properties associated with the solution of the Cauchy problem. Also, the infinite generator of the evolution is nonlocal. For a given arbitrary data in the Sobolev space H(C), it is shown under suitable assumptions that the Goursat problem has a unique solution locally in time. Necessary and sufficient conditions are obtained for the local solution to be \(C^ 2\). The authors have proved estimates from Goursat data to Goursat data, from Goursat data to Cauchy data, and from Cauchy data to Goursat data. Under appropriate conditions, a global solution in H(C) is obtained for the Goursat problem.
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 4152931
zbMATH Keywords: regularity
zbMATH Keywords: Goursat problem
zbMATH Keywords: nonlinear wave equation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Sobolev space
MaRDI profile type: Publication
full work available at URL: 0022-1236(89)90025-6
OpenAlex ID: W2055765670
Wikidata QID: Q62443860
cites work: The global Goursat problem and scattering for nonlinear wave equations
cites work: Solution of the wave equation in \(R^{n+1}\) with data on a characteristic cone
cites work: Q3769302
cites work: Reduction of scattering to an invariant finite displacement in an ambient space-time
description: scientific article; zbMATH DE number 4152931