We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in the context of the 1-d Cahn-Hilliard equation and the current work represents an extension to a higher dimensional problem in which the curvature of the interface plays an important role. The convergence rates obtained are optimal given the assumptions on the initial data.

中文翻译：

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Mullins-Sekerka 问题中平面界面的松弛

我们通过应用基于距离、能量和耗散之间关系的松弛方法来分析 Mullins-Sekerka 模型中平面界面的收敛率。松弛方法是由两位作者在 1-d Cahn-Hilliard 方程的背景下开发的，目前的工作代表了对高维问题的扩展，其中界面的曲率起着重要作用。给定对初始数据的假设，获得的收敛速度是最佳的。