Propagation in a Fisher-KPP equation with non-local advection *
Résumé
We investigate the influence of a general non-local advection term of the form K * u to propagation in the one-dimensional Fisher-KPP equation. This model is a generalization of the Keller-Segel-Fisher system. When K ∈ L 1 (R), we obtain explicit upper and lower bounds on the propagation speed which are asymptotically sharp and more precise than previous works. When K ∈ L p (R) with p > 1 and is non-increasing in (−∞, 0) and in (0, +∞), we show that the position of the " front " is of order O(t p) if p < ∞ and O(e λt) for some λ > 0 if p = ∞ and K(+∞) > 0. We use a wide range of techniques in our proofs.
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