Nonlinear stability results for the modified Mullins-Sekerka and the   surface diffusion flow
  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. 
Emilio Acerbi, Nicola Fusco, Vesa Julin, Massimiliano Morini
math.AP