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Title: On the Stationary Cahn-Hilliard Equation: Bubble Solutions
Authors: Winter, M
Wei, J
Keywords: Bubbles, Exponential Asymptotics,;Phase transition
Issue Date: 1998
Publisher: SIAM
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:Dept of Mathematics Research Papers
Mathematical Sciences

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