Volume 24, Number 3, July–September 2018
|Page(s)||1275 - 1301|
|Published online||13 September 2018|
Motion of discrete interfaces in low-contrast random environments
Technische Universität München,
85748 Garching, Germany
Corresponding author: firstname.lastname@example.org
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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