On Temporal Asymptotics in One-Dimensional Nonlinear Thermoviscoelasticity with Phase Transitions
by
Stephen J. Watson
Louisiana State University

The balance laws of mass, momemtum and energy are considered for a broad class of one dimensional nonlinear thermoviscoelastic materials. For the initial-boundary value problem corresponding to stress free endpoints in the case of a solid, and a specified outer pressure in the case of a gas, we establish new time independent apriori bounds for the deformation gradient. An interesting feature of our analysis is that solid-like and gaseous materials are treated in a unified way. Results on the temporal asymptotics of solutions and there relevance to problems involving change of phase are discussed; numerical simulations are used to illustrate various effects.

Date received: March 31, 1999