Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations

Songmu Zheng; Albert Milani

doi:10.1016/j.na.2004.03.023

Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations

Songmu Zheng, Albert Milani

Mathematics & Statistical Sciences

Research output: Contribution to journal › Article

29 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 exponential attractors and inertial manifolds in the phase space H₀ ¹(0,π)×H^-1(0,π).

Original language	English
Pages (from-to)	843-877
Number of pages	35
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	57
Issue number	5-6
DOIs	https://doi.org/10.1016/j.na.2004.03.023
Publication status	Published - May 1 2004

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.na.2004.03.023

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Zheng, S., & Milani, A. (2004). Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations. Nonlinear Analysis, Theory, Methods and Applications, 57(5-6), 843-877. https://doi.org/10.1016/j.na.2004.03.023

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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 exponential attractors and inertial manifolds in the phase space H0 1(0,π)×H-1(0,π).

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