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Metastability and Layer Dynamics for the Hyperbolic Relaxation of the Cahn–Hilliard Equation.
- Source :
-
Journal of Dynamics & Differential Equations . 2021, Vol. 33 Issue 1, p75-110. 36p. - Publication Year :
- 2021
-
Abstract
- The goal of this paper is to accurately describe the metastable dynamics of the solutions to the hyperbolic relaxation of the Cahn–Hilliard equation in a bounded interval of the real line, subject to homogeneous Neumann boundary conditions. We prove the existence of an approximately invariant manifold M 0 for such boundary value problem, that is we construct a narrow channel containing M 0 and satisfying the following property: a solution starting from the channel evolves very slowly and leaves the channel only after an exponentially long time. Moreover, in the channel the solution has a transition layer structure and we derive a system of ODEs, which accurately describes the slow dynamics of the layers. A comparison with the layer dynamics of the classic Cahn–Hilliard equation is also performed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10407294
- Volume :
- 33
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Dynamics & Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 148519561
- Full Text :
- https://doi.org/10.1007/s10884-019-09806-6