ASYMPTOTIC BEHAVIOR OF THE CAHN-HILLIARD-OONO EQUATION

Alain Miranville

doi:10.11948/2011036

2011 Volume 1 Issue 4

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Alain Miranville. ASYMPTOTIC BEHAVIOR OF THE CAHN-HILLIARD-OONO EQUATION[J]. Journal of Applied Analysis & Computation, 2011, 1(4): 523-536. doi: 10.11948/2011036

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Alain Miranville. ASYMPTOTIC BEHAVIOR OF THE CAHN-HILLIARD-OONO EQUATION[J]. Journal of Applied Analysis & Computation, 2011, 1(4): 523-536. doi: 10.11948/2011036

ASYMPTOTIC BEHAVIOR OF THE CAHN-HILLIARD-OONO EQUATION

Alain Miranville

Laboratoire de Mathématiques et Applications, UMR CNRS 6086-SP2 MI, Boulevard Marie et Pierre Curie-Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France

Abstract

Abstract

Our aim in this article is to study the asymptotic behavior, in terms of finite-dimensional attractors, of the Cahn-Hilliard-Oono equation. This equation differs from the usual Cahn-Hilliard equation by the presence of a term of the form ∊u, ∊>0, which takes into account long-ranged interactions. In particular, we prove the existence of a robust family of exponential attractors as ∊ goes to 0.
- Cahn-Hilliard-Oono equation /
- well-posedness /
- asymptotic behavior /
- global attractor /
- exponential attractor
MSC: 35K55;35J60;80A22

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