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Journal of Mathematical Fluid Mechanics

, Volume 7, Issue 2, pp 153–163 | Cite as

Solutions to a Scalar Discontinuous Conservation Law in a Limit Case of Phase Transitions

  • João-Paulo DiasEmail author
  • Mário Figueira
  • José-Francisco Rodrigues
Original Paper

Abstract.

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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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • João-Paulo Dias
    • 1
    Email author
  • Mário Figueira
    • 1
  • José-Francisco Rodrigues
    • 1
  1. 1.CMAF/ULLisboaPortugal

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