Front Propagation for Reaction–Diffusion Equations in Composite Structures
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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.
KeywordsReaction–diffusion Large deviations Interface motion
Mathematics Subject Classification35K57 35A18 60F10
While working on this article, M. Freidlin was supported by NSF Grant DMS-1411866 and L. Koralov was supported by ARO Grant W911NF1710419.
- 4.Freidlin, M.I.: Propagation of concentration waves due to a random motion connected with growth. Soviet Math. Dokl. 246, 544–548 (1979)Google Scholar
- 12.Freidlin, M.I., Gredeskul, S., Marchenko, A., Pastur, L., Hunter, J.: Wave Front Propagation for KPP-Type Equations. Surveys in Applied Mathematics, vol. 2, pp. 1–62. Plenum Press, Berlin (1995)Google Scholar