Special Session 85: Phase-field models and their singular limits

Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations
Yutaka Terasawa
Nagoya University
Japan
Co-Author(s):    Helmut Abels
Abstract:
We study the nonlocal-to-local convergence for a nonlocal Cahn-Hilliard equation with anisotropic and singular kernels. In particular, we show convergence of weak solutions of the nonlocal Cahn-Hilliard equation to weak solutions of a corresponding anisotropic Cahn-Hilliard equation for suitable subsequences. Moreover, we show existence of weak solutions for the nonlocal equation under a condition, which guarantees existence of weak solutions for suitably localized or singular kernels. We put a focus on the existence part in the talk. This is based on a joint work with Helmut Abels (Regensburg Univ.).