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Journal of Statistical Physics

, Volume 172, Issue 6, pp 1663–1681 | Cite as

Front Propagation for Reaction–Diffusion Equations in Composite Structures

  • M. Freidlin
  • L. Koralov
Article
  • 39 Downloads

Abstract

We consider asymptotic problems concerning the motion of interface separating the regions of large and small values of the solution of a reaction–diffusion equation in the media consisting of domains with different characteristics (composites). Under certain conditions, the motion can be described by the Huygens principle in the appropriate Finsler (e.g., Riemannian) metric. In general, the motion of the interface has, in a sense, non-local nature. In particular, the interface may move by jumps. We are mostly concerned with the nonlinear term that is of KPP type. The results are based on limit theorems for large deviations.

Keywords

Reaction–diffusion Large deviations Interface motion 

Mathematics Subject Classification

35K57 35A18 60F10 

Notes

Acknowledgements

While working on this article, M. Freidlin was supported by NSF Grant DMS-1411866 and L. Koralov was supported by ARO Grant W911NF1710419.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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