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.

中文翻译：

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修正的 Mullins-Sekerka 和表面扩散流的非线性稳定性结果

结果表明，对于面积泛函严格稳定的任何三维周期构型，对于表面扩散流和 Mullins-Sekerka 或 Hele-Shaw 流都是指数稳定的。同样的结果适用于相对于尖锐界面 Ohta-Kawaski 能量严格稳定的三维周期配置。在这种情况下，它们对于所谓的修正 Mullins-Sekerka 流呈指数稳定。