The Cauchy problem for a strongly degenerate quasilinear equation

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, ξ) = ∇ξ f (Z, ξ) and f is a convex function of ξ with linear growth as ∥ξ∥ → ∞, 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. © European Mathematical Society 2005.