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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