Front Propagation for Reaction–Diffusion Equations in Composite Structures

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 b...

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Bibliographic Details
Published in:Journal of statistical physics 2018-09, Vol.172 (6), p.1663-1681
Main Authors: Freidlin, M., Koralov, L.
Format: Article
Language:English
Subjects:
ASYMPTOTIC SOLUTIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Composite structures
COMPUTERIZED SIMULATION
DIFFUSION
DIFFUSION EQUATIONS
Domains
HUYGENS PRINCIPLE
Mathematical and Computational Physics
NONLINEAR PROBLEMS
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Reaction-diffusion equations
RIEMANN SPACE
Statistical Physics and Dynamical Systems
Theoretical
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Description
Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-018-2112-z