On 2X2 systems of conservation laws with fluxes that are entropies

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In this article, we study systems of conservation laws with two dependent and two independent variables which have the property that the fluxes are entropies. Several characterizations of such flux functions are presented. It turns out, that the corresponding systems automatically possess a large class of additional entropies, they are closely related to a kinetic equation, and, in the case of strict hyperbolicity, they can be decoupled into two independent Burgers' equations. The isentropic Euler equations with zero or cubic pressure laws are the most prominent examples of such systems, but other examples are also presented.

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510 Mathematik
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ISO 690JUNK, Michael, 2003. On 2X2 systems of conservation laws with fluxes that are entropies. In: Electronic Journal of Differential Equations. 2003(26), pp. 1-21. eISSN 1072-6691
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@article{Junk2003syste-25421,
  year={2003},
  title={On 2X2 systems of conservation laws with fluxes that are entropies},
  number={26},
  journal={Electronic Journal of Differential Equations},
  pages={1--21},
  author={Junk, Michael}
}
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    <dcterms:abstract xml:lang="eng">In this article, we study systems of conservation laws with two dependent and two independent variables which have the property that the fluxes are entropies. Several characterizations of such flux functions are presented. It turns out, that the corresponding systems automatically possess a large class of additional entropies, they are closely related to a kinetic equation, and, in the case of strict hyperbolicity, they can be decoupled into two independent Burgers' equations. The isentropic Euler equations with zero or cubic pressure laws are the most prominent examples of such systems, but other examples are also presented.</dcterms:abstract>
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