Solutions for the Cahn—Hilliard equation with many boundary spike layers
Published online by Cambridge University Press: 11 July 2007
Abstract
In this paper we construct new classes of stationary solutions for the Cahn–Hilliard equation by a novel approach.
One of the results is as follows. Given a positive integer K and a (not necessarily non-degenerate) local minimum point of the mean curvature of the boundary, then there are boundary K-spike solutions whose peaks all approach this point. This implies that for any smooth and bounded domain there exist boundary K-spike solutions.
The central ingredient of our analysis is the novel derivation and exploitation of a reduction of the energy to finite dimensions (lemma 3.5), where the variables are closely related to the peak locations.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 1 , February 2001 , pp. 185 - 204
- Copyright
- Copyright © Royal Society of Edinburgh 2001
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