Depinning asymptotics in ergodic media

Arnd Scheel; Sergey Tikhomirov

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arXiv · 1610.07102

Depinning asymptotics in ergodic media

Arnd Scheel·Sergey Tikhomirov

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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.

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Arnd Scheel, Sergey Tikhomirov. 2016-10-22. Depinning asymptotics in ergodic media. https://arxiv.org/abs/1610.07102

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