Global attractor for a nonlinear thermoviscoelastic system in shapememory alloys

Extract

This paper is concerned with the existence of a global attractor for a semi-flowgoverned by the weak solutions to a nonlinear one-dimensional thermoviscoelasticsystem with clamped boundary conditions in shape memory alloys. The constitutiveassumptions for the Helmholtz free energy include the model for the study ofmartensitic phase transitions in shape memory alloys. To describe physicallyphase transitions between different configurations of crystal lattices, we workin a framework in which the strain u belongsto L^∞. New approachesare introduced and more delicate estimates are derived to establish the crucialL^∞ -estimate ofstrain u in the course of showing thecompactness of the orbit of the semi-flow and existence of an absorbing set.