Department of Mathematics
Vanderbilt University
Nashville, TN 37240, USA
E-mail address: mayer@math.vanderbilt.edu
Uwe F. Mayer
Abstract:
The (two-sided) Mullins-Sekerka model is a nonlocal evolution model
for closed hypersurfaces, which was originally proposed as a model for
phase transitions of materials of negligible specific heat. Under this
evolution the propagating interfaces maintain the enclosed volume
while the area of the interfaces decreases. We will show by means of an
example that the Mullins-Sekerka flow does not preserve convexity in
two space dimensions, where we consider both the Mullins-Sekerka model
on a bounded domain, and the Mullins-Sekerka model defined on the
whole plane.
Published November 12, 1998.
Mathematics Subject Classifications: 35R35, 35J05, 35B50, 53A07.
Key words and phrases: Mullins-Sekerka flow, Hele-Shaw flow,
Cahn-Hilliard equation, free boundary problem, convexity, curvature.
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Uwe F. Mayer Department of Mathematics Vanderbilt University Nashville, TN 37240, USA E-mail address: mayer@math.vanderbilt.edu |