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Journal of the European Mathematical Society


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Volume 7, Issue 3, 2005, pp. 361–393
DOI: 10.4171/JEMS/32

Published online: 2005-09-30

The Cauchy Problem for a Strongly Degenerate Quasilinear Equation

Fuensanta Andreu[1], Vicent Caselles and José M. Mazón[2]

(1) Universitat de Valencia, Burjassot (Valencia), Spain
(2) Universitat de Valencia, Burjassot (Valencia), Spain

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 $f$ is a convex function of $\xi$ with linear growth as $\Vert \xi\Vert \to\infty$, 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.

Keywords: entropy solution, quasilinear parabolic equation, relativistic heat equation, flux limited diffusion equation, radiation hydrodynamics

Andreu Fuensanta, Caselles Vicent, Mazón José: The Cauchy Problem for a Strongly Degenerate Quasilinear Equation. J. Eur. Math. Soc. 7 (2005), 361-393. doi: 10.4171/JEMS/32