Knopf, Patrik and Signori, Andrea (2021) On the nonlocal Cahn-Hilliard equation with nonlocal dynamic boundary condition and boundary penalization. JOURNAL OF DIFFERENTIAL EQUATIONS, 280. pp. 236-291. ISSN 0022-0396, 1090-2732
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The Cahn-Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. Various dynamic boundary conditions have already been introduced in the literature to model interactions of the materials with the boundary more precisely. To take long-range interactions into account, we propose a new model consisting of a nonlocal Cahn-Hilliard equation with a nonlocal dynamic boundary condition comprising an additional boundary penalization term. We rigorously derive our model as the gradient flow of a nonlocal free energy with respect to a suitable inner product of order H-1 containing both bulk and surface contributions. In the main model, the chemical potentials are coupled by a Robin type boundary condition depending on a specific relaxation parameter. We prove weak and strong well-posedness of this system, and we investigate the singular limits attained when this relaxation parameter tends to zero or infinity. (C) 2021 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Nonlocal Cahn-Hilliard equation; Dynamic boundary conditions; Gradient flow; Asymptotic analysis; Reaction rates; Robin boundary conditions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 10 Aug 2022 11:26 |
| Last Modified: | 10 Aug 2022 11:26 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46439 |
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