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Nonlinear stability of stationary solutions for surface diffusion with boundary conditions

Preprint Series # 864
Garcke, Harald and Ito, Kazuo and Kohsaka, Yoshihito Nonlinear stability of stationary solutions for surface diffusion with boundary conditions. (2007);

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Abstract

The volume preserving fourth order surface diffusion flow has constant mean curvature hypersurfaces as stationary solutions. We show nonlinear stability of certain stationary curves in the plane which meet an exterior boundary with a prescribed contact angle. Methods include semigroup theory, energy arguments, geometric analysis and variational calculus.

Item Type:Preprint
Additional Information:20
Uncontrolled Keywords:surface diffusion, nonlinear stability, energy method, variational calculus
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1723
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