2017/09/04 by Hamel, François, Henderson, Christopher · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1709.00923
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 1/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.