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Asymptotic behavior of the Cahn-Hilliard-Oono equation. (English) Zbl 1304.35342
Summary: 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 \( \epsilon u,\, \epsilon >0\), which takes into account long-ranged interactions. In particular, we prove the existence of a robust family of exponential attractors as \(\epsilon\) goes to \(0\).

MSC:
35K55 Nonlinear parabolic equations
35K59 Quasilinear parabolic equations
35B41 Attractors
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