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A Cahn-Hilliard model in bounded domains with permeable walls. (English) Zbl 1109.35057
The present article proposes a model of phase separation in a binary mixture confined to a bounded region which may be contained within porous walls. The boundary conditions are derived from a mass conservation law and variational methods. Employing classical methods, that is, fixed point theorems and standard energy methods, it is obtained existence and uniqueness of a global solution to the considerd problem. The author compares the presented model of phase separation with other previous Cahn-Hilliard equations with homogeneous Neumann and dynamic boundary conditions.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K55 Nonlinear parabolic equations
74N20 Dynamics of phase boundaries in solids
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