Depner, Daniel and Garcke, Harald
Linearized stability analysis of surface diffusion for hypersurfaces with triple lines.
Preprintreihe der Fakultät Mathematik 15/2011,
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:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||surface diffusion, partial differential equations on manifolds, linearized stability, gradient flow, triple lines|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||18 Apr 2011 06:30|
|Last Modified:||06 Sep 2011 07:04|