Abels, Helmut and Hurm, Christoph (2024) Strong nonlocal-to-local convergence of the Cahn-Hilliard equation and its operator. JOURNAL OF DIFFERENTIAL EQUATIONS, 402. pp. 593-624. ISSN 0022-0396, 1090-2732
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We prove convergence of a sequence of weak solutions of the nonlocal Cahn -Hilliard equation to the strong solution of the corresponding local Cahn -Hilliard equation. The analysis is done in the case of sufficiently smooth bounded domains with Neumann boundary condition and a W 1,1 -kernel. The proof is based on the relative entropy method. Additionally, we prove the strong L 2 -convergence of the nonlocal operator to the negative Laplacian together with a rate of convergence. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC license (http://creativecommons .org /licenses /by -nc /4 .0/).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Cahn-Hilliard equation; Nonlocal Cahn-Hilliard equation; Nonlocal operators; Nonlocal-to-local convergence; Singular limit |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Jul 2025 13:32 |
| Last Modified: | 10 Jul 2025 13:32 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63476 |
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