Archive for Rational Mechanics and Analysis

, Volume 170, Issue 4, pp 359–370

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

Article

DOI: 10.1007/s00205-003-0282-5

Cite this article as:
Perthame, B. & Souganidis, P. Arch. Rational Mech. Anal. (2003) 170: 359. doi:10.1007/s00205-003-0282-5

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Ecole Normale Supérieure DMAUMR8553ParisFrance
  2. 2.Department of MathematicsThe University of Texas at AustinAustinUSA