Abstract

We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity is useful to provide measure valued weak
versus strong uniqueness theorems for the hyperbolic problem. Also, it yields a convergence
result in the zero-viscosity limit to smooth solutions in an Lp framework. The relative en-
tropy identity is also developed for the system of gas dynamics for viscous and heat conducting
gases, and for the system of thermoviscoelasticity with viscosity and heat-conduction. Existing
differences between the example and the general hyperbolic theory are underlined.