Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations
Analysis of PDEs
2025-12-02 v1
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.
Keywords
Cite
@article{arxiv.2512.01545,
title = {Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations},
author = {Helmut Abels and Yutaka Terasawa},
journal= {arXiv preprint arXiv:2512.01545},
year = {2025}
}
Comments
25 pages