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