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On the Stationary Cahn–Hilliard Equation: Interior Spike Solutions

✍ Scribed by Juncheng Wei; Matthias Winter

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
535 KB
Volume
148
Category
Article
ISSN
0022-0396

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✦ Synopsis

We study solutions of the stationary Cahn Hilliard equation in a bounded smooth domain which have a spike in the interior. We show that a large class of interior points (the ``nondegenerate peak'' points) have the following property: There exist such solutions whose spike lies close to a given nondegenerate peak point. Our construction uses among others the methods of viscosity solution, weak convergence of measures, and Liapunov Schmidt reduction.

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