On Hele-Shaw models with surface tension
by
Gieri Simonett, Vanderbilt University
AEB350, 3:15pm Monday, May 20, 1996
Abstract
Of concern is a multi-dimensional moving boundary problem involving
the mean curvature of the unknown moving hypersurface as an explicit
boundary condition. This model is a nonlocal generalization of the
mean curvature flow and is sometimes called Mullins-Sekerka flow.
Using semigroup theory and Fourier multipliers we prove existence and
uniqueness of classical solutions for a large class of initial
surfaces. As a simple consequence it is shown that the Mullins-Sekerka
model is area minimizing and volume preserving.
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