Existence and Nonlocal-to-Local Convergence for Singular, Anisotropic Nonlocal Cahn-Hilliard Equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918225822875648 |
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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 |
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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 |