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2008, Volume 22, Issue 4: 909-932. Doi: 10.3934/dcds.2008.22.909
This issue Previous Article Positive solutions of an integro-differential equation in all space with singular nonlinear term Next Article On a class of elliptic and parabolic equations in convex domains without boundary conditions

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:  August 31, 2007
Revised:  December 31, 2007
Published:  September 2008
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: 35G25, 35B41, 74D10.

    Citation:
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