Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system
type: Item
instance of: scholarly article
title: Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system
zbMATH Open document ID: 1074.35073
DOI: 10.1215/S0012-7094-04-12724-1
published in: Duke Mathematical Journal
publication date: 2005-06-09T00:00:00Z
review text: This paper deals with the Cauchy problem for a system of conservation laws with a particular class of flux functions in \(m\) space dimensions. It is shown that initial data, with arbitrarily small total variations and uniformly close to a non-zero constant, such that the BV norm of admissible solution blows up instantaneously, no matter what criterion of admissibility is chosen among the ones proposed in the literature. In certain cases this occurs unless the system reduces to decoupled transport equations with constant coefficients. This work should be of interest to some one working on conservation laws.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 2174753
zbMATH Keywords: Cauchy problem
zbMATH Keywords: bounded variation (BV) norm
zbMATH Keywords: blow up of solutions
zbMATH Keywords: transport equations
zbMATH Keywords: conservation laws
author: Camillo De Lellis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2174753