TY - JOUR
T1 - Slow and fast minimal speed traveling waves of the FKPP equation with chemotaxis
AU - Henderson, Christopher
N1 - Funding Information:
The author is grateful to Alexander Kiselev and Francois Hamel for helpful discussions early in the development of this work at the Banff workshop “Interacting Particle Systems and Parabolic PDEs.” This work was partially supported by NSF grants DMS-2003110 and DMS-2204615.
Publisher Copyright:
© 2022 Elsevier Masson SAS
PY - 2022/11
Y1 - 2022/11
N2 - We examine a general model for the Fisher-KPP (FKPP) equation with nonlocal advection. The main interpretation of this model is as describing a diffusing and logistically growing population that is also influenced by intraspecific attraction or repulsion. For a particular choice of parameters, this specializes to the Keller-Segel-Fisher equation for chemotaxis. Our interest is in the effect of chemotaxis on the speed of traveling waves. We prove that there is a threshold such that, when interactions are weaker and more localized than this, chemotaxis, despite being non-trivial, does not influence the speed of traveling waves; that is, the minimal speed traveling wave has speed 2 as in the FKPP case. On the other hand, when the interaction is repulsive, we show that the minimal traveling wave speed is arbitrarily large in a certain asymptotic regime in which the interaction strength and length scale tend to infinity.
AB - We examine a general model for the Fisher-KPP (FKPP) equation with nonlocal advection. The main interpretation of this model is as describing a diffusing and logistically growing population that is also influenced by intraspecific attraction or repulsion. For a particular choice of parameters, this specializes to the Keller-Segel-Fisher equation for chemotaxis. Our interest is in the effect of chemotaxis on the speed of traveling waves. We prove that there is a threshold such that, when interactions are weaker and more localized than this, chemotaxis, despite being non-trivial, does not influence the speed of traveling waves; that is, the minimal speed traveling wave has speed 2 as in the FKPP case. On the other hand, when the interaction is repulsive, we show that the minimal traveling wave speed is arbitrarily large in a certain asymptotic regime in which the interaction strength and length scale tend to infinity.
KW - Chemotaxis
KW - Fisher-KPP
KW - Minimal speed
KW - Pushed and pulled fronts
KW - Traveling waves
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U2 - 10.1016/j.matpur.2022.09.004
DO - 10.1016/j.matpur.2022.09.004
M3 - Article
AN - SCOPUS:85139866550
VL - 167
SP - 175
EP - 203
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
ER -