The Cauchy Problem for a Strongly Degenerate Quasilinear Equation
Fuensanta Andreu
Universitat de Valencia, Burjassot (Valencia), SpainVicent Caselles
Universitat Pompeu-Fabra, Barcelona, SpainJosé M. Mazón
Universitat de Valencia, Burjassot (Valencia), Spain
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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