Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions: Nonlinear dynamics



- Stanislaus Maier-Paape, Thomas Wanner:
Spinodal decomposition for the Cahn-Hilliard equation in higher dimensions: Nonlinear dynamics
Archive for Rational Mechanics and Analysis 151(3), pp. 187-219, 2000.
Abstract
This paper addresses the phenomenon of spinodal decomposition for the Cahn-Hilliard equation in , subject to on , where , , is a bounded domain with sufficiently smooth boundary, and is cubic-like, for example . Based on the results of Maier-Paape, Wanner (1998) the nonlinear Cahn-Hilliard equation will be discussed. This equation generates a nonlinear semiflow in certain affine subspaces of . In a neighborhood with size proportional to around the constant solution , where lies in the spinodal region, we observe the following behavior. Within a local inertial manifold containing there exists a finite-dimensional invariant manifold which dominates the behavior of all solutions starting with initial conditions from a small ball around with probability almost . The dimension of is proportional to and the elements of exhibit a common geometric quantity which is strongly related to a characteristic wavelength proportional to .
Links
The published version of the paper can be found at https://doi.org/10.1007/s002050050196.
Bibtex
@article{maier:wanner:00a,
author = {Stanislaus Maier-Paape and Thomas Wanner},
title = {Spinodal decomposition for the {C}ahn-{H}illiard equation in
higher dimensions: {N}onlinear dynamics},
journal = {Archive for Rational Mechanics and Analysis},
year = 2000,
volume = 151,
number = 3,
pages = {187--219},
doi = {10.1007/s002050050196}
}