Continuous Glimm-type functionals and spreading of rarefunction waves
type: Item
instance of: scholarly article
title: Continuous Glimm-type functionals and spreading of rarefunction waves
zbMATH Open document ID: 1094.35077
author: Konstantina Trivisa
author: Philippe G. LeFloch
published in: Communications in Mathematical Sciences
publication date: 2006-02-08T00:00:00Z
review text: Several Glimm-type functionals for (piecewise smooth) approximate solutions of nonlinear hyperbolic systems have been introduced in recent years. In this paper, following a work by Baiti and Bressan on genuinely nonlinear systems we provide a framework to prove that such lower semi-continuity properties with respect to the strong \(L^1\) topology. In particular, our result applies to the functionals introduced by Iguchi-LeFloch and Liu-Yang for systems with general flux-functions, as well as the functional introduced by Baiti-LeFloch-Piccoli for nonclassical entropy solutions. As an illustration of the use of continuous Glimm-type functionals, we also extend a result by Bressan and Colombo for genuinely nonlinear systems, and establish an estimate on the spreading of rarefaction waves in solutions of hyperbolic systems with general flux-function.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35L60
zbMATH DE Number: 5004807
zbMATH Keywords: nonclassical solutions
zbMATH Keywords: total variation
MaRDI profile type: Publication
full work available at URL: cms.2004.v2.n2.a5
OpenAlex ID: W2004886661
DOI: 10.4310/CMS.2004.V2.N2.A5
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description: scientific article; zbMATH DE number 5004807