Uniqueness and long-time behavior for the conserved system with memory

Abstract.

This paper is concerned with a conserved model with memory. We include memory by replacing the standard Fourier heat law with a constitutive assumption of Gurtin_Pipkin type, and the system is conservative in the sense that the initial mass of the order parameter as well as the energy are preserved during the evolution. A Cauchy_Neumann problem is investigated for this model which couples a Volterra integro_differential equation with fourth order dynamics for the phase field. A sharp uniqueness theorem is proven by demonstrating continuous dependence for a suitably weak formulation. With regard to the \ , the limit points of the trajectories are completely characterized.

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