Global existence and asymptotic behavior in nonlinear thermoviscoelasticity

Abstract

We study global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to the system of nonlinear thermoviscoelasticity. Various boundary conditions are considered. It is shown that for any initial data (u0, v0, θ0) ε L∞ × W1,∞ × H1 there is a unique global solution (u, v, θ) = (deformation gradient, velocity, temperature) such that u ε C([0, ∞], L∞), v ε C((0, ∞), W1,∞) ∩L∞([0, ∞), W1,∞), θεC([0, ∞), H1). The constitutive assumptions for the Helmholtz free energy include the models for the study of phase transition problems in shape memory alloys. © 1997 Academic Press.