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Global attractor for a nonlinear thermoviscoelastic model with a non-convex free energy density
Authors:Yuming Qin  Jianan Fang
Institution:1. Department of Applied Mathematics, College of Science, Donghua University, Shanghai 200051, PR China;2. College of Information Science, Donghua University, Shanghai 200051, PR China
Abstract: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 uu belongs to LL. New approaches are introduced and more delicate estimates are derived to establish the crucial LL-estimate of strain uu in deriving the compactness of the orbit of the semiflow and the existence of an absorbing set.
Keywords:35Q72  35B40  73B30  74H40  74D10  74F05
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