Abels, Helmut and Kampmann, J. (2020) On a model for phase separation on biological membranes and its relation to the Ohta-Kawasaki equation. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 31 (2). pp. 297-338. ISSN 0956-7925, 1469-4425
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We provide a detailed mathematical analysis of a model for phase separation on biological membranes which was recently proposed by Garcke, Ratz, Roger and the second author. The model is an extended Cahn-Hilliard equation which contains additional terms to account for the active transport processes. We prove results on the existence and regularity of solutions, their long-time behaviour, and on the existence of stationary solutions. Moreover, we investigate two different asymptotic regimes. We study the case of large cytosolic diffusion and investigate the effect of an infinitely large affinity between membrane components. The first case leads to the reduction of coupled bulk-surface equations in the model to a system of surface equations with non-local contributions. Subsequently, we recover a variant of the well-known Ohta-Kawasaki equation as the limit for infinitely large affinity between membrane components.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | RAFT FORMATION; FREE-ENERGY; MECHANISMS; SYSTEM; Partial differential equations on surfaces; phase separation; Cahn-Hilliard equation; Ohta-Kawasaki equation; reaction-diffusion systems |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Mar 2021 05:36 |
| Last Modified: | 29 Mar 2021 05:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44816 |
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