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

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  • This paper is concerned with a conserved phase-field 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 long-time behavior, the limit points of the trajectories are completely characterized.
    Mathematics Subject Classification: 35R99, 45K05, 80A22.


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