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|Title:||On the Stationary Cahn-Hilliard Equation: Bubble Solutions|
|Keywords:||Bubbles, Exponential Asymptotics,;Phase transition|
|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|
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