In this paper, a multi-layered interface system is introduced, which is formally derived by a singular limit of a weakly coupled system of the Allen–Cahn type equation. By using the level set approach, this system is written as a quasi-monotone degenerate parabolic system with discontinuous functions. The well-posedness of viscosity solutions is shown, and the singularity of particular viscosity solutions is discussed.

中文翻译：

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多层接口系统的水平集方法

在本文中，介绍了一个多层接口系统，该系统是通过艾伦-卡恩型方程的弱耦合系统的奇异极限形式正式得出的。通过使用水平集方法，该系统被编写为具有不连续函数的准单调简并抛物线系统。显示了粘度溶液的适定性，并讨论了特定粘度溶液的奇异性。