Issue |
ESAIM: COCV
Volume 24, Number 3, July–September 2018
|
|
---|---|---|
Page(s) | 1275 - 1301 | |
DOI | https://doi.org/10.1051/cocv/2017067 | |
Published online | 13 September 2018 |
Motion of discrete interfaces in low-contrast random environments
Technische Universität München,
Boltzmannstrasse 3,
85748 Garching, Germany
Corresponding author: mruf@ma.tum.de
Received:
9
February
2017
Accepted:
10
October
2017
We study the asymptotic behavior of a discrete-in-time minimizing movement scheme for square lattice interfaces when both the lattice spacing and the time step vanish. The motion is assumed to be driven by minimization of a weighted random perimeter functional with an additional deterministic dissipation term. We consider rectangular initial sets and lower order random perturbations of the perimeter functional. In case of stationary, α-mixing perturbations we prove a stochastic homogenization result for the interface velocity. We also provide an example which indicates that only stationary, ergodic perturbations might not yield a spatially homogenized limit velocity for this minimizing movement scheme.
Mathematics Subject Classification: 53C44 / 49J55 / 49J45
Key words: Minimizing movement / discrete interface motion / crystalline curvature / stochastic homogenization
© EDP Sciences, SMAI 2018
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