Differential Equations and Computational Simulations III
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 171179.
Twosided MullinsSekerka flow does not preserve convexity
Uwe F. Mayer
Abstract:
The (twosided) MullinsSekerka 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 MullinsSekerka flow does not preserve convexity in
two space dimensions, where we consider both the MullinsSekerka model
on a bounded domain, and the MullinsSekerka model defined on the
whole plane.
Published November 12, 1998.
Mathematics Subject Classifications: 35R35, 35J05, 35B50, 53A07.
Key words and phrases: MullinsSekerka flow, HeleShaw flow,
CahnHilliard equation, free boundary problem, convexity, curvature.
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Uwe F. Mayer
Department of Mathematics
Vanderbilt University
Nashville, TN 37240, USA
Email address: mayer@math.vanderbilt.edu

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