Garcke, Harald and Lam, Kei Fong and Nürnberg, Robert and Signori, Andrea (2025) On a Cahn-Hilliard equation for the growth and division of chemically active droplets modelling protocells. EUROPEAN JOURNAL OF APPLIED MATHEMATICS. ISSN 0956-7925, 1469-4425
Full text not available from this repository. (Request a copy)Abstract
The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size. This phenomenon has been suggested as a model for protocells, and a model based on the modified Cahn-Hilliard equation has been formulated. We introduce this equation and show the existence and uniqueness of solutions. Then, formally matched asymptotic expansions are used to identify a sharp interface limit using a scaling of the reaction term, which becomes singular when the interfacial thickness tends to zero. We compute planar solutions and study their stability under non-planar perturbations. Numerical computations for the suggested model are used to validate the sharp interface asymptotics. In addition, the numerical simulations show that the reaction terms lead to diverse phenomena such as growth and division of droplets in the obtained solutions, as well as the formation of shell-like structures.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; PHASE FIELD MODEL; TUMOR-GROWTH; SYSTEM; CONVERGENCE; CHEMOTAXIS; Cahn-Hilliard equation; chemical reactions; pattern formation; active droplets; protocells |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 May 2026 05:31 |
| Last Modified: | 07 May 2026 05:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67004 |
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