The Dirichlet boundary problem for a nonlocal Cahn–Hilliard equation

We study the existence, uniqueness and continuous dependence on initial data of the solution for a nonlocal Cahn–Hilliard equation with Dirichlet boundary condition on a bounded domain. Under a nondegeneracy assumption the solutions are classical but when this is relaxed, the equation is satisfied i...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2005-11, Vol.311 (1), p.289-312
Main Authors: Bates, Peter W., Han, Jianlong
Format: Article
Language:English
Subjects:
Absorbing set
Exact sciences and technology
Global attractor
Long range interaction
Mathematical analysis
Mathematics
Nonlocal parabolic partial differential equation
Partial differential equations
Phase transition
Sciences and techniques of general use
Well-posedness
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Summary:We study the existence, uniqueness and continuous dependence on initial data of the solution for a nonlocal Cahn–Hilliard equation with Dirichlet boundary condition on a bounded domain. Under a nondegeneracy assumption the solutions are classical but when this is relaxed, the equation is satisfied in a weak sense. Also we prove that there exists a global attractor in some metric space.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2005.02.041