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Propagation in Fisher-KPP type equations with fractional diffusion in periodic media (1209.4809v1)
Published 21 Sep 2012 in math.AP
Abstract: 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-G\"artner formula for the standard Laplacian.