Knopf, Patrik and Stange, Jonas (2025) Strong well-posedness and separation properties for a bulk-surface convective Cahn-Hilliard system with singular potentials. JOURNAL OF DIFFERENTIAL EQUATIONS, 439: 113408. ISSN 0022-0396, 1090-2732
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This paper addresses the well-posedness of a general class of bulk-surface convective Cahn-Hilliard systems with singular potentials. For this model, we first prove the existence of a global-in-time weak solution by approximating the singular potentials via a Yosida regularization, applying the corresponding results for regular potentials, and eventually passing to the limit in this approximation scheme. Then, we prove the uniqueness of weak solutions and their continuous dependence on the velocity fields and the initial data. Afterwards, assuming additional regularity of the domain as well as the velocity fields, we establish higher regularity properties of weak solutions and eventually the existence of strong solutions. In the end, we discuss strict separation properties for logarithmic type potentials in both two and three dimensions. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DYNAMIC BOUNDARY-CONDITIONS; ROBUST EXPONENTIAL ATTRACTORS; OPTIMAL VELOCITY CONTROL; EQUATION; MODEL; CONVERGENCE; Convective Cahn-Hilliard equation; Bulk-surface interaction; Dynamic boundary conditions; Strong solutions; Separation property; Yosida approximation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Jun 2026 05:49 |
| Last Modified: | 16 Jun 2026 05:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65918 |
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