On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions

João-Paulo Dias; Mário Figueira

doi:10.3934/cpaa.2004.3.53

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2004, Volume 3, Issue 1: 53-58. Doi: 10.3934/cpaa.2004.3.53

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On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions

João-Paulo Dias^1, and
Mário Figueira^1,

1.
CMAF/UL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa

Received: January 31, 2003

Revised: July 31, 2003

Published: February 2004

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Abstract

For a special class of discontinuous flux functions that can be associated to the limit case of a phase transition it has been introduced in [2] an appropriate notion of entropy weak solution to the Cauchy problem and some existence results were proved. In this paper, for the discontinuous scalar case, we give a counter-example to uniqueness and we prove an estimate based in Kruskov's method. Then, for a class of discontinuous $p$-systems, we prove, by applying a variant of the regularization method introduced by Dafermos in [1], an existence result for the Riemann problem.

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Mathematics Subject Classification: 35L45, 35L65.

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