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Archive for Rational Mechanics and Analysis

, Volume 147, Issue 4, pp 269–361 | Cite as

Entropy Solutions for Nonlinear Degenerate Problems

  • José Carrillo
Article

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.

Keywords

Boundary Condition Entropy Continuous Function General Condition Vectorial Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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