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Richness and the Classification of Quasilinear Hyperbolic Systems

  • Denis Serre
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 29)

Abstract

Rich quasilinear hyperbolic systems are those which possess the largest possible set of entropies. Such systems have a property of global existence of weak solutions, whatever large is the bounded initial data. Although the full gas dynamics is not rich, many physically meaningful systems are. One gives below new examples and properties of the fully linearly degenerate case.

Keywords

Weak Solution Cauchy Problem Global Existence Smooth Solution Young Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Résumé

Un essai de classification des systèmes quasilinéaires hyperboliques conduit à considérer ceux dont 1’ ensemble d’ entropies est aussi grand que le permettent des considérations immédiates. Ces systèmes, dits riches, ont des solutions faibles globales pour des données initiales bornées. Bien que la dynamique des gaz n’ entre pas dans cette catégorie, de nombreux systemes ayant un sens physique sont riches. On donne ci — dessous de nouveaux exemples et on étudie dans cette famille la dégénérescence linéaire des champs caractéristiques.

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Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Denis Serre
    • 1
  1. 1.Ecole Normale Supérieure de LyonLyon Cedex 07France

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