Archive for Rational Mechanics and Analysis

, Volume 147, Issue 4, pp 269–361

Entropy Solutions for Nonlinear Degenerate Problems

  • José Carrillo
Article

DOI: 10.1007/s002050050152

Cite this article as:
Carrillo, J. Arch Rational Mech Anal (1999) 147: 269. doi:10.1007/s002050050152

Abstract

. We consider a class of elliptic‐hyperbolic degenerate equations \(g(u)-\Delta b(u) +\divg\phi (u) =f\) with Dirichlet homogeneous boundary conditions and a class of elliptic‐parabolic‐hyperbolic degenerate equations \(g(u)_t-\Delta b(u) +\divg\phi (u) =f\) with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function φ satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for φ continuous.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • José Carrillo
    • 1
  1. 1.Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain, e‐mail: carrillo@sunma4.mat.ucm.esES

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