Global existence and asymptotic behavior of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions

This paper is concerned with global existence, uniqueness, and asymptotic b ehavior, as time tends to infinity, of weak solutions to nonlinear thermovi scoelastic systems with clamped boundary conditions. The constitutive assum ptions for the Helmholtz free energy include the model for the study of pha se transitions in shape memory alloys. To describe phase transitions betwee n different configurations of crystal lattices, we work in a framework in w hich the strain u belongs to L-infinity. It is shown that for any initial d ata of (strain, velocity, absolute temperature) (u(0), v(0), theta(0)) is a n element of L-infinity x W-0(1,infinity) x H-1, there is a unique global s olution (u, v, theta) is an element of C([0, +infinity]; L-infinity) x C(0, +infinity); W-0(1,infinity)) boolean AND L-infinity([0, +infinity); W-1,W- infinity) x C([0, +infinity); H-1). Results concerning the asymptotic behav ior as time goes to infinity are obtained. A new approach is introduced and more delicate estimates are derived to obt ain the crucial L-infinity-norm estimate of u.