Linearized stability analysis of surface diffusion for hypersurfaces with boundary contact
Daniel Depner · Mathematische Nachrichten · 2012
Abstract 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.