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|Title:||Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers|
|Keywords:||Nonlinear Elliptic Equations;Phase Transition|
|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|
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