Zusammenfassung
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 ...
Zusammenfassung
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.
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