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.
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