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We show that there exist traveling wave solutions of the Keller-Segel-FKPPequation, which models a diffusing and logistically growing population subjectto chemotaxis. In contrast to previous results, our result is in the strongaggregation regime; that is, we make no smallness assumption on the parameters.The lack of a smallness condition makes $L^\infty$-estimates difficult toobtain as the comparison principle no longer gives them ``for free." Instead,our proof is based on suitable energy estimates in a carefully tailoreduniformly local $L^p$-space. Interestingly, our uniformly local space involvesa scaling parameter, the choice of which is a crux of the argument. Numericalexperiments exploring the stability, qualitative properties, and speeds ofthese waves are presented as well.

Traveling waves for the Keller-Segel-FKPP equation with strong chemotaxis