The Cauchy Problem for a Strongly Degenerate Quasilinear Equation
Vicent Caselles
Universitat Pompeu-Fabra, Barcelona, SpainFuensanta Andreu
Universitat de Valencia, Burjassot (Valencia), SpainJosé 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 \( u_t = \div \, \a(u,Du) \), where \( \a(z,\xi) = \nabla_\xi f(z,\xi) \), 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
Vicent Caselles, Fuensanta Andreu, 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