New results on traveling waves for the Keller–Segel model with logistic source

Abstract

We study the existence of traveling waves for the Keller–Segel chemotaxis system with logistic source in parabolic–parabolic and parabolic–elliptic cases. By a unified approach, we obtain new results on the traveling waves of these systems, via a novel constructive method and applying Schauder’s fixed point theorem. These findings can be further applied to study the spreading behaviors and estimate the spreading speed of the systems.