Depinning asymptotics in ergodic media
Pattern Formation and Solitons
2017-02-17 v2 Dynamical Systems
Abstract
We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent depending a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are satisfied in a context of weak inhomogeneity of the medium and almost balanced kinetics, and compare asymptotics with numerical simulations.
Keywords
Cite
@article{arxiv.1610.07102,
title = {Depinning asymptotics in ergodic media},
author = {Arnd Scheel and Sergey Tikhomirov},
journal= {arXiv preprint arXiv:1610.07102},
year = {2017}
}
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17 pages