ASYMPTOTIC BEHAVIOR OF THE CAHN-HILLIARD-OONO EQUATION
By Alain Miranville. 2011
58 citations recorded by the source corpus.
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 \(0\).
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/790a7806ddc6ab9bc89230f55de95699165d68c3
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Materials Chemistry
Citations in the corpus
- A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “In [54], it was also shown that, in certain sense (i.e., the existence of a robust family of exponential attractors as χ → 0 + ), the dynamics of the original Cahn–Hilliard equation is “close” to that of the Cahn–Hilliard–Oono equation, for χ > 0 being su ffi ciently small.”