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Acceleration in reaction-diffusion equations

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If you have a question about this talk, please contact Harsha Hutridurga .

Widely used in mathematical biology, reaction-diffusion equations, and in particular the Fisher-KPP equation, are used to model the spreading of a population through a new environment. The earliest results showed that populations moved at a constant speed (i.e. linear in time). However, about five years ago, Hamel and Roques discovered acceleration, or super-linear in time propagation of the population, when the initial population is very spread out. Over the last few years, acceleration has been discovered in a number of other settings. In this talk, I will discuss several of these settings, with the aim of developing an intuition for what causes and what blocks acceleration. The work in this talk is joint with Emeric Bouin and Lenya Ryzhik.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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