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December  2008, 22(4): 909-932. doi: 10.3934/dcds.2008.22.909

Uniform attractors for a phase transition model coupling momentum balance and phase dynamics

1. 

Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, I-27100 Pavia

2. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin

Received  September 2007 Revised  January 2008 Published  September 2008

In this paper we are concerned with the uniform attractor for a nonautonomous dynamical system related to the Frémond thermo-mechanical model of shape memory alloys. The dynamical system consists of a diffusive equation for the phase proportions coupled with the hyperbolic momentum balance equation, in the case when a damping term is considered in the latter and the temperature field is prescribed. We prove that the solution to the related initial-boundary value problem yields a semiprocess which is continuous on the proper phase space and satisfies a dissipativity property. Then we show the existence of a unique compact and connected uniform attractor for the system.
Citation: Pierluigi Colli, Antonio Segatti. Uniform attractors for a phase transition model coupling momentum balance and phase dynamics. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 909-932. doi: 10.3934/dcds.2008.22.909
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