Calculus of Variations and Geometric Measure Theory
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G. Scilla - F. Solombrino

Multiscale analysis of singularly perturbed finite dimensional gradient flows: the minimizing movement approach

created by scilla on 17 Dec 2017
modified on 27 Dec 2017

[BibTeX]

Submitted Paper

Inserted: 17 dec 2017
Last Updated: 27 dec 2017

Year: 2017

ArXiv: 1712.06182 PDF

Abstract:

We perform a multiscale analysis of a finite dimensional singularly perturbed gradient flow by solving a discrete-in-time minimization scheme. When the ratio between the viscosity parameter and the time scale diverges, we rigorously prove the convergence to a Balanced Viscosity solution of the stationary problem. We also characterize the limit evolution corresponding to an asymptotically finite ratio between the scales, describing the behaviour at the jumps by means of a discrete crease energy.

Keywords: singular perturbations, Gradient Flow, Variational methods, rate-independent systems, minimizing movement, Balanced Viscosity solutions, crease energy


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