The Cauchy Problem for a Strongly Degenerate Quasilinear Equation

  • Fuensanta Andreu

    Universitat de Valencia, Burjassot (Valencia), Spain
  • Vicent Caselles

    Universitat Pompeu-Fabra, Barcelona, Spain
  • José M. Mazón

    Universitat de Valencia, Burjassot (Valencia), Spain

Abstract

We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation , where , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics.

Cite this article

Fuensanta Andreu, Vicent Caselles, José M. Mazón, The Cauchy Problem for a Strongly Degenerate Quasilinear Equation. J. Eur. Math. Soc. 7 (2005), no. 3, pp. 361–393

DOI 10.4171/JEMS/32