AN EXISTENCE AND UNIQUENESS RESULT FOR FLUX LIMITED DIFFUSION EQUATIONS

作者：Caselles Vicent^*

来源：Discrete and Continuous Dynamical Systems, 2011, 31(4): 1151-1195.

DOI：10.3934/dcds.2011.31.1151

• Degenerate parabolic equations
• Flux Limited Diffusion
• nonlinear semigroup

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) is an element of BV(R(N)), u(0) >= 0, where a(z, xi) = del(xi) f(z, xi) and f is a convex function of xi with linear growth as parallel to xi parallel to -> infinity, 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.

• 出版日期2011-12