ELASTIC PHASE-TRANSITIONS - A NEW MODEL

In this note we consider a new model for one-dimensional elastic phase transitions. The model is described by two hyperbolic systems: one wh ich propagates information at speeds +/-c and the other at speeds +/-l ambda where lambda > c > 0. The model supports slow-moving under-compr essive shocks which connect separate phases of the material and micros tructural equilibrium solutions similar to those predicted by viscosit y-capillarity theories for such materials. Our principal results are c ontained in Section 3 and describe the long-term behavior of the syste m. Section 4 presents numerical simulations for our model for a variet y of initial and boundary conditions. These results confirm the analys is of Sections 2 and 3.