Global attractor for a nonlinear thermoviscoelastic model with a non-convex free energy density

This paper is concerned with the existence of a global attractor for a semiflow governed by the weak solutions to a nonlinear one-dimensional thermoviscoelasticity with a non-convex free energy density. The constitutive assumptions for the Helmholtz free energy include the model for the study of martensitic phase transitions in shape memory alloys. To describe physically phase transitions between different configurations of crystal lattices, we work in a framework in which the strain u$u$ belongs to L^∞$L^{\infty }$. New approaches are introduced and more delicate estimates are derived to establish the crucial L^∞$L^{\infty }$-estimate of strain u$u$ in deriving the compactness of the orbit of the semiflow and the existence of an absorbing set.