Istituto di Matematica Applicata e Tecnologie Informatiche     
Rocca E. Existence and Uniqueness for the Parabolic Conserved Phase Field Model with Memory. Preprint ercim.cnr.ian//2001-1207, 2001.
A nonlinear system for the heat diffusion inside a material subject to a phase change is considered. The underlying model is a generalized version of the well-known Caginalp conserved phase-field system, where the Fourier law is replaced by the Coleman-Gurtin heat flux law and a linear growth is allowed for the latent heat density. The resulting problem couples a non-linear parabolic equation derived from the balance of energy with a fourth order parabolic inclusion which rules the evolution of the order parameter $chi$. Homogeneous Neumann boundary conditions guarantee that the space-average of $chi$ is conserved in time. Existence and uniqueness of the solution are proved.
Subject 35R99, 45K05, 80A22

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