An existence and uniqueness result for flux limited diffusion equations

Vicent Caselles

doi:10.3934/dcds.2011.31.1151

Article Contents

2011, Volume 31, Issue 4: 1151-1195. Doi: 10.3934/dcds.2011.31.1151

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An existence and uniqueness result for flux limited diffusion equations

Vicent Caselles^1,

1.
DTIC, Universitat Pompeu Fabra, C/Roc Boronat 138, 08018 Barcelona

Received: November 2009

Revised: January 2010

Published: October 2011

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Abstract

We prove existence and uniqueness of entropy solutions of the Cauchy problem for the quasilinear parabolic equation $u_t$ $= div$ $a$$(u,Du)$ with initial condition $u_0$ $\in BV(\mathbb{R}^N)$, $u_0$$\geq 0$, 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 that cover the case of the so-called relativistic heat equation and other flux limited diffusion equations used in the theory of radiation hydrodynamics.

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Mathematics Subject Classification: Primary: 35K55; Secondary: 35K15, 35B40.

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