I will present the research I have done with Dr. Henderson. The equations we studied model a diffusing and logistically growing population subject to chemotaxis (e.g., the migration of bacteria in the presence of glucose and alcohol). We show that traveling wave solutions exist for this model, but, in contrast to previous considerations, we make no assumption on the strength of the chemotaxis. Without this assumption, L∞-estimates are difficult to obtain, so an alternative approach is taken by obtaining energy estimates in “uniformly local Lp-spaces.” Numerical simulations demonstrating the qualitative nature of solutions to this model are also presented.

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