Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations

Fuente: arXiv
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Main Authors: Abels, Helmut, Terasawa, Yutaka
Format: Preprint
Published: 2025
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author Abels, Helmut
Terasawa, Yutaka
author_facet Abels, Helmut
Terasawa, Yutaka
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_01545
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations
Abels, Helmut
Terasawa, Yutaka
Analysis of PDEs
45K05, 35B40, 35K61
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.
title Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations
topic Analysis of PDEs
45K05, 35B40, 35K61
url https://arxiv.org/abs/2512.01545