Depner, Daniel and Garcke, Harald (2013) Linearized stability analysis of surface diffusion for hypersurfaces with triple lines. HOKKAIDO MATHEMATICAL JOURNAL, 42 (1). pp. 11-52. ISSN 0385-4035,
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The linearized stability of stationary solutions for surface diffusion is studied. We consider three hypersurfaces that lie inside a fixed domain and touch its boundary with a right angle and fulfill a non-flux condition. Additionally they meet at a triple line with prescribed angle conditions and further boundary conditions resulting from the continuity of chemical potentials and a flux balance have to hold at the triple line. We introduce a new specific parametrization with two parameters corresponding to a movement in tangential and normal direction to formulate the geometric evolution law as a system of partial differential equations. For the linearized stability analysis we identify the problem as an H-1-gradient flow, which will be crucial to show self-adjointness of the linearized operator. Finally we study the linearized stability of some examples.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CONSTANT MEAN-CURVATURE; STATIONARY SOLUTIONS; BOUNDARY-CONDITIONS; CAPILLARY SURFACES; MOTION; FLOW; surface diffusion; partial differential equations on manifolds; linearized stability; gradient flow; triple lines |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 24 Apr 2020 07:54 |
| Last Modified: | 24 Apr 2020 07:54 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17164 |
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