Depner, Daniel (2012) Linearized stability analysis of surface diffusion for hypersurfaces with boundary contact. MATHEMATISCHE NACHRICHTEN, 285 (11-12). pp. 1385-1403. ISSN 0025-584X,
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The linearized stability of stationary solutions for surface diffusion is studied. We consider hypersurfaces that lie inside a fixed domain, touch its boundary with a right angle and fulfill a no-flux condition. We formulate the geometric evolution law as a partial differential equation with the help of a parametrization from Vogel 24, which takes care of a possible curved boundary. For the linearized stability analysis we identify as in the work of Garcke, Ito and Kohsaka 14 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; CAPILLARY SURFACES; EQUATIONS; MOTION; FLOW; Partial differential equations on manifolds; surface diffusion; linearized stability of stationary solutions; gradient flow; msc (2010) 35G30; 35R35; 35B35 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 May 2020 05:59 |
| Last Modified: | 08 May 2020 05:59 |
| URI: | https://pred.uni-regensburg.de/id/eprint/18391 |
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