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Memory relaxation of the one-dimensional cahn-hilliard equation

Dissipative Phase Transitions, ISSN: 1793-0901, Page: 101-114
2006
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  • Citations
    13
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      13

Book Chapter Description

We consider the memory relaxation of the one-dimensional Cahn-Hilliard equation, endowed with the no-flux boundary conditions. The resulting integrodifferential equation is characterized by a memory kernel, which is the rescaling of a given positive decreasing function. The Cahn-Hilliard equation is then viewed as the formal limit of the relaxed equation, when the scaling parameter (or relaxation time) ε tends to zero. In particular, if the memory kernel is the decreasing exponential, then the relaxed equation is equivalent to the standard hyperbolic relaxation. The main result of this paper is the existence of a family of robust exponential attractors for the one-parameter dissipative dynamical system generated by the relaxed equation. Such a family is stable with respect to the singular limit ε → 0.

Bibliographic Details

Stefania Gatti; Maurizio Grasselli; Vittorino Pata; Alain Miranville

World Scientific Pub Co Pte Lt

Mathematics; Physics and Astronomy

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