Uniqueness of Weak Solutions to the Phase-Field Model with Memory

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 3, Page 459--476.

Colli, Pierluigi ; Laurençot, Philippe
Uniqueness of Weak Solutions to the Phase-Field Model with Memory
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Abstract:
The paper deals with a phase-field model based on the Gurtin-Pipkin heat flux law. A Volterra integrodifferential equation is coupled with a nonlinear parabolic equation in the resulting system, associated with a set of initial and Neumann boundary conditions. Uniqueness of the solution is proved when the convolution kernel is just supposed to be of positive type. Some regularity results are also derived.

Mathematics Subject Classification (1991): 35G25, 45K05, 80A22
Mathematical Reviews Number: MR1656061

Received: 1997-08-08