Electron. J. Diff. Eqns. Vol. 1993(1993), No. 08, pp. 1-7.

One-sided Mullins-Sekerka flow does not preserve convexity

Uwe F. Mayer

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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Uwe F. Mayer
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112 USA
e-mail: mayer@csc-sun.math.utah.edu
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