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. 361–393DOI 10.4171/JEMS/32