Rachidi B. Salako, Wenxian Shen
This article concerns traveling wave solutions of the fully parabolic Keller-Segel chemotaxis system with logistic source,
where are positive numbers, and . Among others, it is proved that if and , then for every , this system has a traveling wave solution (for all ) connecting the two constant steady states and , and there is no such solutions with speed less than , which improves the results established in  and shows that this system has a minimal wave speed , which is independent of the chemotaxis.
Submitted August 11, 2019. Published May 27, 2020.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: Parabolic chemotaxis system; logistic source; traveling wave solution; minimal wave speed.
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| Rachidi B. Salako |
Department of Mathematics
The Ohio State University
Columbus, OH 43210-1174, USA
| Wenxian Shen |
Department of Mathematics and Statistics
Auburn, AL 36849, USA
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