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 language | English (US) |
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Title of host publication | Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday |
Editors | Pavel Gurevich, Juliette Hell, Arnd Scheel, Bjorn Sandstede |
Publisher | Springer New York LLC |
Pages | 88-108 |
Number of pages | 21 |
ISBN (Print) | 9783319641720 |
DOIs | |
State | Published - 2017 |
Event | Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016 - Berlin, Germany Duration: Jul 25 2016 → Jul 29 2016 |
Publication series
Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 205 |
ISSN (Print) | 2194-1009 |
ISSN (Electronic) | 2194-1017 |
Other
Other | Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016 |
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Country/Territory | Germany |
City | Berlin |
Period | 7/25/16 → 7/29/16 |
Bibliographical note
Funding Information: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.
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.
Publisher Copyright:
© Springer International Publishing AG 2017.
Keywords
- Center manifolds
- Ergodic media
- Front propagation
- Inhomogeneous media
- Pinning
- Quasiperiodic media