Solutions to a Scalar Discontinuous Conservation Law in a Limit Case of Phase Transitions
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For a particular discontinuous flux function that can be associated to the limit case of a phase transition, we introduce an appropriate notion of entropy weak solution to the Cauchy problem for the corresponding conservation law. Then, for a class of initial data, that includes the Riemann data, we prove, by the vanishing viscosity method and with a suitable regularisation of the flux function, the existence of an entropy weak solution. This result can be easily extended to more general flux functions.
Mathematics Subject Classification (2000).35L65
Keywords.Scalar conservation laws phase transitions
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