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Proceedings of the American Mathematical Society

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Dynamics of a parabolic-ODE competition system in heterogeneous environments


Authors: Yuan Lou and Rachidi B. Salako
Journal: Proc. Amer. Math. Soc. 148 (2020), 3025-3038
MSC (2010): Primary 92D25, 35B40, 35K57
DOI: https://doi.org/10.1090/proc/14972
Published electronically: March 17, 2020
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Abstract: This work is concerned with the large time behavior of the solutions of a parabolic-ODE hybrid system, modeling the competition of two populations which are identical except for their movement behaviors: one species moves by random dispersal while the other does not diffuse. We show that the non-diffusing population will always drive the diffusing one to extinction in environments with sinks. In contract, the non-diffusing and diffusing populations can coexist in environments without sinks.


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Additional Information

Yuan Lou
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: lou@math.ohio-state.edu

Rachidi B. Salako
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: salako.7@osu.edu

DOI: https://doi.org/10.1090/proc/14972
Keywords: Competition system, reaction-diffusion, asymptotic behavior
Received by editor(s): September 28, 2019
Received by editor(s) in revised form: December 6, 2019
Published electronically: March 17, 2020
Additional Notes: This research was supported in part by NSF grant DMS-1853561
Communicated by: Wenxian Shen
Article copyright: © Copyright 2020 American Mathematical Society