Depinning asymptotics in ergodic media

2016/10/22 by Scheel, Arnd, Tikhomirov, Sergey · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)

paper · doi:10.48550/arxiv.1610.07102

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.

Cited by

• Travelling front solutions in a spatially heterogeneous reaction-diffusion system

Related

• Slow-fast systems in infinite measure, with or without averaging
• Asymptotic analysis of a monostable equation in periodic media
• Bistable pulsating fronts in slowly oscillating environments *
• Propagating speeds of bistable transition fronts in spatially periodic media
• KPP Front Speeds in Random Shears and the Parabolic Anderson Problem