Reaction-diffusion and propagation in non-homogenous media - Abstract: The classical theory of reaction-diffusion deals with nonlinear parabolic equations that are homogenous in space and in time. It analyses travelling waves, long time behavior and the speed of propagation. More general, heterogeneous reaction-diffusion equations arise naturally in models of ecology, biology and medicine that lead to challenging mathematical questions. In this series of lectures, after reviewing fundamental results of the classical theory, I will describe recent progress on models that involve spatially heterogeneous non-linear parabolic and elliptic equations. I will also consider cases with non-local diffusions. The course will involve the following themes: 1. Review of the classical theory of homogenous reaction-diffusion equations. 2. The effect of a line with fast diffusion on Fisher-KPP invasion. 3. The effect of domain shape. 4. Models with non-local operators. 5. Propagation and spreading speeds in non-homogeneous media.
This seminar has been delivered by Professor Henri Berestycki, Directeur d'études, EHESS, at IMPA - Instituto Nacional de Matemática Pura e Aplicada
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