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Title: | Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers |
Authors: | Winter, M Wei, J |
Keywords: | Nonlinear Elliptic Equations;Phase Transition |
Issue Date: | 2001 |
Publisher: | Cambridge University Press |
Citation: | Winter, M. and Wei, J. (2001) 'Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers', Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 131(1), pp. 185-204. doi:10.1017/S0308210500000834. |
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 nondegenerate) 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 loations. |
URI: | http://bura.brunel.ac.uk/handle/2438/519 |
DOI: | https://doi.org/10.1017/s0308210500000834 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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