Global attractors for singular perturbations of the Cahn-Hilliard equations

Songmu Zheng; Albert Milani

doi:10.1016/j.jde.2004.08.026

Global attractors for singular perturbations of the Cahn-Hilliard equations

Songmu Zheng, Albert Milani

Mathematics & Statistical Sciences

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49 Citations (Scopus)

Abstract

We consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn-Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space H₀^l (0, π) × H^-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.

Original language	English
Pages (from-to)	101-139
Number of pages	39
Journal	Journal of Differential Equations
Volume	209
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2004.08.026
Publication status	Published - Feb 1 2005

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2004.08.026

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abstract = "We consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn-Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.",

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AB - We consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn-Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.

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Global attractors for singular perturbations of the Cahn-Hilliard equations

Abstract

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