Abels, Helmut and Garcke, Harald and Mueller, Lars (2016) Local well-posedness for volume-preserving mean curvature and Willmore flows with line tension. MATHEMATISCHE NACHRICHTEN, 289 (2-3). pp. 136-174. ISSN 0025-584X, 1522-2616
Full text not available from this repository. (Request a copy)Abstract
We show the short-time existence and uniqueness of solutions for the motion of an evolving hypersurface in contact with a solid container driven by the volume-preserving mean curvature flow (MCF) taking line tension effects on the boundary into account. Difficulties arise due to dynamic boundary conditions and due to the contact angle and the non-local nature of the resulting second order, nonlinear PDE. In addition, we prove the same result for the Willmore flow with line tension, which results in a nonlinear PDE of fourth order. For both flows we will use a curvilinear cordinate system due to Vogel to write the flows as graphs over a fixed reference hypersurface.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NEUMANN BOUNDARY-CONDITION; RED-BLOOD-CELL; L-P-REGULARITY; PARABOLIC PROBLEMS; SURFACES; ENERGY; HYPERSURFACES; CONVERGENCE; STABILITY; Mean curvature flow; Willmore flow; well-posedness; dynamic boundary conditions; line energy; geodesic curvature flow; maximal regularity; 53C44; 35K35; 35K55 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Mar 2019 07:17 |
| Last Modified: | 14 Mar 2019 07:17 |
| URI: | https://pred.uni-regensburg.de/id/eprint/2467 |
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