Global Existence and Asymptotic Behavior in Nonlinear Thermoviscoelasticity

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) L∞×W1, ∞×H1there is a unique global solution (u, v, θ)=(deformation gradient, velocity, temperature) such thatu C([0, ∞], L∞),v C((0, ∞), W1, ∞)∩L∞([0, ∞), W1, ∞),θ C([0, ∞), H1). The constitutive assumptions for the Helmholtz free energy include the models for the study of phase transition problems in shape memory alloys.