Propagation in a Fisher-KPP equation with non-local advection
Propagation in a Fisher-KPP equation with non-local advection
复制标题
DOI：
10.1016/j.jfa.2019.108426
复制
发表时间：
2020-04-15
影响因子：
1.7
通讯作者：
Henderson, Christopher
中科院分区：
文献类型：
--
作者：
Hamel, Francois;Henderson, Christopher
我们研究了形如$K*u$的一般非局部平流项对一维Fisher - KPP方程中传播的影响。该模型是Keller - Segel - Fisher系统的一种推广。当$K\in L^1(\mathbb{R})$时，我们得到了传播速度的显式上下界，这些界是渐近精确的，且比先前的研究更精确。当$K\in L^p(\mathbb{R})$且$p>1$，并且在$(-\infty,0)$和$(0,+\infty)$上非递增时，我们表明如果$p<\infty$，“前沿”的位置是$O(t^p)$阶的；如果$p = \infty$且$K(+\infty)>0$，则是$O(e^{\lambda t})$（对于某个$\lambda>0$）。我们在证明过程中使用了多种技术。© 2019爱思唯尔公司。保留所有权利。
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 is an element of 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 is an element of L-P(R) with p > 1 and is non-increasing in (-infinity, 0) and in (0, +infinity), we show that the position of the "front" is of order 0(t(p)) if p < infinity and O(e(lambda t)) for some lambda > 0 if p = infinity and K(+infinity) > 0. We use a wide range of techniques in our proofs. (C) 2019 Elsevier Inc. All rights reserved.