Abstract:Phase field models are widely adopted to describe evolutions of interfaces in continuum mechanics. They can be constructed to purposely reproduce a given sharp interface model when the thickness of the diffused interface tends to zero. As a type of non-parametric models, they can describe topological changes of interfaces and display sophisticated patterns. In this mini-course we shall focus on the simplest phase field model, namely the parabolic Allen-Cahn equation, and study its convergence to mean curvature flow. A tentative list of topics is as follows:

Lecture 1: Asymptotic expansion method for the Allen–Cahn equations. The modulated energy method and Modica’s maximum principle.   Time :2022-10-23 14:00-16:00

Lecture 2: Monotonicity of Gaussian density functional and convergence to Brakke’s flows.  Time :2022-10-30  14:00-16:00

Lecture 3: The relative entropy method and a sharp convergence rate estimate. Time :2022-11-06  14:00-16:00

Lecture 4: Analysis of vectorial and anisotropic models. Time :2022-11-13 14:00-16:00

Lecture 5: Other related models. Time :2022-11-20  14:00-16:00

Tencent Meeting：https://meeting.tencent.com/dm/ixBrYCBM0p9m

Meeting ID：609-7731-5183