We study the asymptotic limit of diffused surface energy in the van der Waals–Cahn–Hillard theory when an advection term is added and the energy is uniformly bounded. We prove that the limit interface is an integral varifold and the generalized mean curvature vector is determined by the advection term. As the application, a prescribed mean curvature problem is solved using the min–max method.

中文翻译：

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Sobolev空间中具有对流项的扩散界面

当添加对流项并且能量被均匀地限制时，我们在范德华斯-卡恩-希尔拉德理论中研究了扩散表面能的渐近极限。我们证明了极限界面是一个整体的曲率，而广义平均曲率矢量是由对流项决定的。作为应用，使用最小-最大方法解决了规定的平均曲率问题。