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Convergence of the Cahn–Hilliard Equation to the Mullins–Sekerka Problem in Spherical Symmetry

✍ Scribed by Barbara E.E. Stoth

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 822 KB
Volume: 125
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.0028

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✦ Synopsis

We show that, as = Ä 0, the solution of the Cahn Hilliard equation

converges to a solution of the Mullins Sekerka problem &2u=0 in each phase,

where & denotes a normal, V the normal velocity and K the sum of principal curvatures of the interface, provided the solutions are radially symmetric. We use energy type estimates to show that the solution of the Cahn Hilliard equation can be approximated by the well known stationary wave solution that corresponds to the potential W.

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