Depinning asymptotics in ergodic media

Arnd Scheel, Sergey Tikhomirov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

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 on 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.

Original languageEnglish (US)
Title of host publicationPatterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday
EditorsPavel Gurevich, Juliette Hell, Arnd Scheel, Bjorn Sandstede
PublisherSpringer New York LLC
Pages88-108
Number of pages21
ISBN (Print)9783319641720
DOIs
StatePublished - 2017
EventConference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016 - Berlin, Germany
Duration: Jul 25 2016Jul 29 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume205
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherConference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016
CountryGermany
CityBerlin
Period7/25/167/29/16

Bibliographical note

Funding Information:
Acknowledgements. A. Scheel was partially supported through NSF grants DMS-1612441 and DMS-1311740, through a DAAD Faculty Research Visit Grant, WWU Fellowship, and a Humboldt Research Award. S. Tikhomirov would like to thank JSC “Gazprom neft” and Contest “Young Russian Mathematics” for their attention to this work.

Keywords

  • Center manifolds
  • Ergodic media
  • Front propagation
  • Inhomogeneous media
  • Pinning
  • Quasiperiodic media

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