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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: Proc Roy Soc Edinburgh Sect A 131 (2001), 185-204
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.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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