TRAVELING WAVES IN A RELAXATION SYSTEM

Certain phase transitions are modeled as conservation laws with a non- monotone stress-strain relation. The governing equations are, then, of mixed type. Additional constitutive assumptions are required to formu late a mathematically well posed system of equations. Examples of such regularization include viscosity, visco-capillarity, viscoelasticity, and kinetic phase boundary relations. Here we regularize by adding a viscoelastic relaxation term. We examine Riemann problems and travelin g wave solutions of the mixed system. In particular, we show that for certain data, the relaxation system admits a solution not seen by visc osity-visco-capillarity admissibility criteria. For these data, a gene ralization of the Oleinik-Liu entropy condition admits the same soluti on as does viscoelastic relaxation.