An example of non-uniqueness for a hyperbolic equation with non-Lipschitz-continuous coefficients.
type: Item
instance of: scholarly article
title: An example of non-uniqueness for a hyperbolic equation with non-Lipschitz-continuous coefficients.
zbMATH Open document ID: 1148.35334
author: Ferruccio Colombini
author: Daniele Del Santo
published in: Journal of Mathematics of Kyoto University
publication date: 2003-10-29T00:00:00Z
review text: A second order strictly hyperbolic linear partial differential operator \(P\) in the \(n+1\) dimensional Euclidean space is considered. If the coefficients in the principal part of the operator satisfy the Lipschitz condition, then P has the uniqueness in the Cauchy problem. In [\textit{F. Colombini}, \textit{E. Jannelli} and \textit{S. Spagnolo}, Non-uniqueness in hyperbolic Cauchy problems, Ann. Math. (2) 126, 495--524 (1987; Zbl 0649.35051)], one shows the existence of hyperbolic operators with Hölder continuous coefficients in the principal part that does not have the uniqueness property. In the present article one tries to improve the above result by better pointing out the connection between the regularity of the coefficients in the principal part of the operator and the uniqueness in the Cauchy problem.
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 1998379
zbMATH Keywords: uniqueness
zbMATH Keywords: Cauchy problem
zbMATH Keywords: regularity of coefficients
reviewed by: Claudia Simionescu-Badea
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250283848
OpenAlex ID: W1643853006
DOI: 10.1215/KJM/1250283848
description: scientific article; zbMATH DE number 1998379