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June 2004 Coninuous Glimm-Type Functionals and Spreading of Rarefaction Waves
Philippe G. Lefloch, Andkonstantina Trivisa
Commun. Math. Sci. 2(2): 213-236 (June 2004).


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 functionals can be extended to general functions with bounded variation and we investigate their lower semi-continuity properties with respect to the strong L1topology. 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.


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Philippe G. Lefloch. Andkonstantina Trivisa. "Coninuous Glimm-Type Functionals and Spreading of Rarefaction Waves." Commun. Math. Sci. 2 (2) 213 - 236, June 2004.


Published: June 2004
First available in Project Euclid: 1 March 2005

zbMATH: 1094.35077
MathSciNet: MR2119939

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 2 • June 2004
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