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Depinning Asymptotics in Ergodic Media

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Patterns of Dynamics (PaDy 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 205))

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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 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.

Dedicated to Professor Bernold Fiedler on the occasion of his 60th birthday.

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church St. S.E, Minneapolis, MN, 55455, USA

    Arnd Scheel

  2. St.Petersburg State University, 7/9 Universitetskaya Nab, St. Petersburg, 199034, Russia

    Sergey Tikhomirov

Authors
  1. Arnd Scheel
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  2. Sergey Tikhomirov
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Correspondence to Arnd Scheel .

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Editors and Affiliations

  1. Mathematical Institute, Free University of Berlin, Berlin, Germany

    Pavel Gurevich

  2. Mathematical Institute, Free University of Berlin, Berlin, Germany

    Juliette Hell

  3. Division of Applied Mathematics, Brown University, Providence, Rhode Island, USA

    Björn Sandstede

  4. School of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA

    Arnd Scheel

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Scheel, A., Tikhomirov, S. (2017). Depinning Asymptotics in Ergodic Media. In: Gurevich, P., Hell, J., Sandstede, B., Scheel, A. (eds) Patterns of Dynamics. PaDy 2016. Springer Proceedings in Mathematics & Statistics, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-319-64173-7_6

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