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Carnegie Mellon NSF logoCenter for Nonlinear Analysis
Jean-Michel Roquejoffre
Afilliation: Institut de Mathématiques, Université de Toulouse

Title: The Logarithmic Shift in Fisher-KPP Equations

Abstract: In a famous 1937 paper, Kolmogorov, Petrovskii and Piskunov proved that the solution of the Fisher equation, with heaviside initial datum, converges to a critical (i.e. with slowest speed) wave, modulo some time shift. This shift was proved to be logarithmic in time by Bamson, via probabilistic arguments. We will explain how we can understand this result with PDE tools, and discuss how it generalises to spatially inhomogeneous models. Joint work with F. Hamel, J. Nolen, L. Ryzhik.