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March  2004, 3(1): 53-58. doi: 10.3934/cpaa.2004.3.53

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, Portugal, Portugal

Received  February 2003 Revised  August 2003 Published  January 2004

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.
Keywords: phase transitions., discontinuous system, Riemann problem.
Mathematics Subject Classification: 35L45, 35L6.
Citation: João-Paulo Dias, Mário Figueira. On the Riemann problem for some discontinuous systems of conservation laws describing phase transitions. Communications on Pure and Applied Analysis, 2004, 3 (1) : 53-58. doi: 10.3934/cpaa.2004.3.53
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