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3‐D viscous Cahn–Hilliard equation with memory
Author(s) -
Conti Monica,
Mola Gianluca
Publication year - 2008
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.1091
Subject(s) - cahn–hilliard equation , mathematics , scaling , attractor , exponential function , relaxation (psychology) , viscosity , kernel (algebra) , zero (linguistics) , mathematical analysis , term (time) , pure mathematics , partial differential equation , thermodynamics , geometry , physics , psychology , social psychology , linguistics , philosophy , quantum mechanics
We deal with the memory relaxation of the viscous Cahn–Hilliard equation in 3‐D, covering the well‐known hyperbolic version of the model. We study the long‐term dynamic of the system in dependence of the scaling parameter of the memory kernel ε and of the viscosity coefficient δ. In particular we construct a family of exponential attractors, which is robust as both ε and δ go to zero, provided that ε is linearly controlled by δ. Copyright © 2008 John Wiley & Sons, Ltd.