Department of Mathematical Sciences

Center for Nonlinear Analysis

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Publication 14-CNA-012

Motion of Three-Dimensional Elastic Films by Anisotropic Surface Diffusion with Curvature Regularization

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Nicola Fusco
Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
Università degli Studi di Napoli "Federico II"
Napoli, Italy
n.fusco@unina.it

Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
giovanni@andrew.cmu.edu

Massimiliano Morini
Dipartimento di Matematica
Università degli Studi di Parma
Parma, Italy
massimiliano.morini@unipr.it

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 low 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.

Get the paper in its entirety as 14-CNA-012.pdf

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