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Propagation in Fisher-KPP type equations with fractional diffusion in periodic media. (English. Abridged French version) Zbl 1253.35198
Summary: We are interested in the time asymptotic location of the level sets of solutions to Fisher-KPP reaction-diffusion equations with fractional diffusion in periodic media. We show that the speed of propagation is exponential in time, with a precise exponent depending on a periodic principal eigenvalue, and that it does not depend on the space direction. This is in contrast with the Freidlin-Gärtner formula for the standard Laplacian.

35R11 Fractional partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
Full Text: DOI arXiv
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