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Non-local Cahn–Hilliard equations with fractional dynamic boundary conditions

Published online by Cambridge University Press:  01 December 2016

CIPRIAN G. GAL
CIPRIAN G. GAL*
Affiliation:
Department of Mathematics & Statistics, Florida International University, Miami, FL 33199, USA email: cgal@fiu.edu
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Abstract

We consider a non-local version of the Cahn–Hilliard equation characterized by the presence of a fractional diffusion operator, and which is subject to fractional dynamic boundary conditions. Our system generalizes the classical system in which the dynamic boundary condition was used to describe any relaxation dynamics of the order-parameter at the walls. The proposed fractional dynamic boundary condition appears to be more general in the sense that it incorporates non-local effects which were completely ignored in the classical approach. We aim to deduce well-posedness and regularity results as well as to establish the existence of finite-dimensional attractors for this system.

Keywords

Non-local Cahn–Hilliard equationfractional dynamic boundary conditionsregional fractional Laplacianfractional Wentzell Laplacianwell-posednessregularityglobal attractor

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 5 , October 2017 , pp. 736 - 788
Copyright
Copyright © Cambridge University Press 2016 

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