Uwe F. Mayer
Abstract: The Mullins-Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn-Hilliard equation. Assuming the existence of sufficiently smooth solutions we will show that the one-sided Mullins-Sekerka flow does not preserve convexity.
Submitted November 6, 1993. Published December 13, 1993.
Math Subject Classification: 35R35, 35J05, 35B50, 53A07.
Key Words: Mullins-Sekerka flow, Hele-Shaw flow, Cahn-Hilliard equation,
free boundary problem, convexity, curvature.
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