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Nonlinear stability results for the modified Mullins–Sekerka and the surface diffusion flow
Journal of Differential Geometry  (IF2.688),  Pub Date : 2019-09-01, DOI: 10.4310/jdg/1567216953
E. Acerbi, N. Fusco, V. Julin, M. Morini

It is shown that any three-dimensional periodic configuration that is strictly stable for the area functional is exponentially stable for the surface diffusion flow and for the Mullins-Sekerka or Hele-Shaw flow. The same result holds for three-dimensional periodic configurations that are strictly stable with respect to the sharp-interface Ohta-Kawaski energy. In this case, they are exponentially stable for the so-called modified Mullins-Sekerka flow.