Weak solutions to a phase-field model with non-constant thermal conductivity

Laurençot, Ph.

doi:10.1090/qam/1486546

Author: Ph. Laurençot
Journal: Quart. Appl. Math. 55 (1997), 739-760
MSC: Primary 35Q99; Secondary 35D05, 80A22
DOI: https://doi.org/10.1090/qam/1486546
MathSciNet review: MR1486546
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Abstract: We investigate the existence of weak solutions to a phase-field model when the thermal conductivity vanishes for some values of the order parameter. We obtain weak solutions for a general class of free energies, including non-differentiable ones. We also study the $\omega$-limit set of these weak solutions, and investigate their convergence to a solution of a degenerate Cahn-Hilliard equation.

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