Electronic Journal of Differential Equations,
Conference 01 (1998), pp. 171-179

Title: Two-sided Mullins-Sekerka flow 

Authors: Uwe F. Mayer (Vanderbilt Univ., Nashville, TN, USA)
 
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.
Math Subject Classifications: 35R35,
35J05, 35B50, 53A07
Key Words: Mullins-Sekerka flow; Hele-Shaw flow; Cahn-Hilliard equation; free boundary problem; convexity; curvature.