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|Title: ||Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers|
|Authors: ||Winter, M|
|Keywords: ||Nonlinear Elliptic Equations|
|Publication 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
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
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:||Mathematical Science|
Dept of Mathematics Research Papers
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