A Contractive Metric for Systems of Conservation Laws with Coinciding Shock and Rarefaction Curves

A. Bressan

doi:10.1006/jdeq.1993.1111

A Contractive Metric for Systems of Conservation Laws with Coinciding Shock and Rarefaction Curves

A. Bressan

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We introduce two algorithms for the construction of weak, entropy-admissible solutions to a class of systems of conservation laws with coinciding shock and rarefaction curves. Global existence, uniqueness, and continuous dependence are proved for all solutions obtained by our constructive procedure. The generated semigroup is contractive with respect to a Riemann-type metric, defined in terms of Glimm′s wave interaction functional, equivalent to the usual L₁ distance.

Original language	English (US)
Pages (from-to)	332-366
Number of pages	35
Journal	Journal of Differential Equations
Volume	106
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1993.1111
State	Published - Dec 1993

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1006/jdeq.1993.1111

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abstract = "We introduce two algorithms for the construction of weak, entropy-admissible solutions to a class of systems of conservation laws with coinciding shock and rarefaction curves. Global existence, uniqueness, and continuous dependence are proved for all solutions obtained by our constructive procedure. The generated semigroup is contractive with respect to a Riemann-type metric, defined in terms of Glimm′s wave interaction functional, equivalent to the usual L1 distance.",

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AB - We introduce two algorithms for the construction of weak, entropy-admissible solutions to a class of systems of conservation laws with coinciding shock and rarefaction curves. Global existence, uniqueness, and continuous dependence are proved for all solutions obtained by our constructive procedure. The generated semigroup is contractive with respect to a Riemann-type metric, defined in terms of Glimm′s wave interaction functional, equivalent to the usual L1 distance.

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JO - Journal of Differential Equations

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A Contractive Metric for Systems of Conservation Laws with Coinciding Shock and Rarefaction Curves

Abstract

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