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Analysis
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Alexis L?culier, RLM 10.176: Propagation in a fractional reaction-diffusion equation in a periodic hostile environment
Friday, March 15, 2019, 01:00pm - 02:00pm
The question studied here is the large time behavior of the solutionsn(t,x) of the non-local reaction-diffusion equation ∂_tn+(−∆)^α n = n−n^2, posed in a periodicdomain composed of disconnected intervals. Such equation modelsthe growth and the invasion of a species subject to a non-localdispersion in an environment that has hostile patches. The functionn stands for the density of the population. The fractional Laplaciandescribes the motions of individuals, it takes into account thepossibility of "jump" (move rapidly) of individuals from onepoint to another. Contrary to what happens for standard diffusionα = 1, there is here a unique bounded stationary state thatinvades the domain exponentially fast. Joint work with S. Mirrahimiand J.M. Roquejoffre.
Location: RLM 10.176

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