Abels, Helmut and Buerger, Felicitas and Garcke, Harald (2023) Short time existence for coupling of scaled mean curvature flow and diffusion. JOURNAL OF EVOLUTION EQUATIONS, 23 (1): 14. ISSN 1424-3199, 1424-3202
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We prove a short time existence result for a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss a mean curvature flow scaled with a term that depends on a quantity defined on the surface coupled to a diffusion equation for that quantity. The proof is based on a splitting ansatz, solving both equations separately using linearization and a contraction argument. Our result is formulated for the case of immersed hypersurfaces and yields a uniform lower bound on the existence time that allows for small changes in the initial value of the height function.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SURFACE; DRIVEN; Mean curvature flow; Diffusion equation on surfaces; Geometric evolution equation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Feb 2024 10:55 |
| Last Modified: | 29 Feb 2024 10:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59200 |
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