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Dissipative and Entropy Solutions to Non-Isotropic Degenerate Parabolic Balance Laws

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Abstract.

We propose a new notion of weak solutions (dissipative solutions) for non-isotropic, degenerate, second-order, quasi-linear parabolic equations. This class of solutions is an extension of the notion of dissipative solutions for scalar conservation laws introduced by L. C. Evans. We analyze the relationship between the notions of dissipative and entropy weak solutions for non-isotropic, degenerate, second-order, quasi-linear parabolic equations. As an application we prove the strong convergence of a general relaxation-type approximation for such equations.

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Authors and Affiliations

  1. Ecole Normale Supérieure DMA, UMR8553, 45 rue d’Ulm, 75230, Paris, France

    Benoît Perthame

  2. Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA

    P. E. Souganidis

Authors
  1. Benoît Perthame
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  2. P. E. Souganidis
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Corresponding author

Correspondence to Benoît Perthame.

Additional information

Communicated by L. C. Evans

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Perthame, B., Souganidis, P. Dissipative and Entropy Solutions to Non-Isotropic Degenerate Parabolic Balance Laws. Arch. Rational Mech. Anal. 170, 359–370 (2003). https://doi.org/10.1007/s00205-003-0282-5

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  • DOI: https://doi.org/10.1007/s00205-003-0282-5

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