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|Title: ||On the Stationary Cahn-Hilliard Equation: Bubble Solutions|
|Authors: ||Winter, M|
|Keywords: ||Bubbles, Exponential Asymptotics,|
|Publication Date: ||1998|
|Citation: ||SIAM J Math Anal 29 (1998), 1492-1518|
|Abstract: ||We study
stationary solutions of the Cahn--Hilliard equation in a bounded
smooth domain which have an interior spherical interface (bubbles).
We show that a large class of interior points
(the ``nondegenerate peak'' points)
have the following property: there exists such a
solution whose bubble center lies close to a given nondegenerate peak point.
Our construction uses among others the Liapunov-Schmidt
reduction method and exponential asymptotics.|
|Appears in Collections:||Mathematical Science|
Dept of Mathematics Research Papers
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