This paper is concerned with the existence of a global attractor for a semi-flow
governed by the weak solutions to a nonlinear one-dimensional thermoviscoelastic
system with clamped boundary conditions in shape memory alloys. 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 belongs
to L∞. New approaches
are introduced and more delicate estimates are derived to establish the crucial
L∞ -estimate of
strain u in the course of showing the
compactness of the orbit of the semi-flow and existence of an absorbing set.