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Motion of
three-dimensional elastic films by anisotropic surface
diffusion with curvature regularization
Irene Fonseca, Nicola Fusco, Giovanni Leoni and Massimiliano Morini |
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Vol. 8 (2015), No. 2, 373–423
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Abstract |
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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 -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, gradient flows,
higher order geometric flows, elastically stressed
epitaxial films, volume-preserving evolution, long-time
behavior, Liapunov stability
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Mathematical Subject Classification 2010
Primary: 35K25, 53C44, 74K35, 35Q74
Secondary: 37B25
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Milestones
Received: 9 May 2014
Accepted: 22 January 2015
Published: 10 May 2015
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Authors |
| Irene Fonseca | |
| Department of Mathematical
Sciences Carnegie Mellon University Pittsburgh, PA 15213 United States |
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| Nicola Fusco | |
| Dipartimento di Matematica e
Applicazioni “R. Caccioppoli” Università degli Studi di Napoli “Federico II” I-80126 Napoli Italy |
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| Giovanni Leoni | |
| Department of Mathematical
Sciences Carnegie Mellon University Pittsburgh, PA 15213 United States |
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| Massimiliano Morini | |
| Dipartimento di Matematica Università degli Studi di Parma I-43121 Parma Italy |
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