VISCOELASTIC RELAXATION WITH A VAN-DER-WAALS TYPE STRESS

Contemporary science models certain phase transitions as conservation laws with a non-monotone stress-strain relation. The system of conserv ation laws are often hyperbolic except in a region in phase space, whe re the system is elliptic or of composite type. It is possible to prov e existence and uniqueness of solutions for specific models which exhi bit such change of type, but notions of admissibility and the connecti ons between the mathematical theory and engineering experiments are no t fully understood. In this paper we model phase transition by a visco -clastic relaxation law, and describe numerical experiments on this sy stem. In particular we examine special initial data which, in the cont ext of the mixed system, gives rise to multiple solutions.