DEPNER Daniel, GARCKE Harald,
Linearized stability analysis of surface diffusion for hypersurfaces with triple lines.
Hokkaido Mathematical Journal, 42 (2013) pp.11-52
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.
|MSC(Secondary)||35R35, 35B35, 35K55, 53C44|
|Uncontrolled Keywords||surface diffusion, partial differential equations on manifolds, linearized stability, gradient flow, triple lines|