Existence of relaxation shock profiles for hyperbolic conservation laws

In this paper we prove that, like viscosity, relaxation can also smooth wea k shocks for strict hyperbolic conservation laws as equilibium systems of h yperbolic relaxation systems under some natural structural conditions. Thes e conditions were derived previously by Yong from stability considerations and hence are entirely analogous to the Majda-Pego criterion of the viscous case. The proof involves a new parametrization of Hugoniot curves and a de licate analysis of the algebraic structure of relaxation systems as well as construction of an appropriate center manifold.