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Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions
Author(s) -
Miranville A.,
Zelik S.
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.590
Subject(s) - mathematics , cahn–hilliard equation , uniqueness , attractor , boundary (topology) , mathematical analysis , boundary value problem , exponential function , parabolic partial differential equation , partial differential equation
Abstract We consider in this article the Cahn–Hilliard equation endowed with dynamic boundary conditions. By interpreting these boundary conditions as a parabolic equation on the boundary and by considering a regularized problem, we obtain, by the Leray–Schauder principle, the existence and uniqueness of solutions. We then construct a robust family of exponential attractors. Copyright © 2005 John Wiley & Sons, Ltd.