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Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions

URN to cite this document:
urn:nbn:de:bvb:355-epub-109622
Garcke, Harald ; Ito, Kazuo ; Yoshihito, Kohsaka
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Date of publication of this fulltext: 20 Nov 2009 07:02


Abstract

The linearized stability of stationary solutions to the surface diffusion flow with angle and no-flux boundary conditions is studied. In this linearized stability analysis the $H^{-1}$ gradient flow structure plays a key role. As a byproduct the analysis also gives a criterion for the stability of critical points of the length functional of curves which come into contact with the outer boundary. Some examples of linearized stability are studied as well.


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