Submitted Paper

Inserted: 8 may 2014
Last Updated: 23 may 2014

Year: 2014

Abstract:

Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.

Keywords: minimizing movements, surface diffusion, epitaxial films, Liapunov stability

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• 3d-evolution-2014-05-17.pdf