1:00 pm Wednesday, May 4, 2016
Analysis Seminar: Large time behaviour in Fisher-KPP type equations by
Jean-Michel Roquejoffre [mail] (Institut de Mathématiques, Université Paul Sabatier) in RLM 10.176
The Fisher-KPP (Kolmogorov, Petrovskii, Piskunov) in one spatial variable is one of the simplest looking reaction-diffusion equations. The solution starting from a Heaviside initial datum will converge, up to a nontrivial logarithmic time delay, to a travelling wave. This result was proved by Bramson in the early 80's, using elaborate probabilistic arguments. We will present a simple PDE proof of this result, and discuss some extensions, such as sharp asymptotics, or time-inhomogeneous equations where the delay is not logarithmic in time anymore. Submitted by
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