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Uniqueness and global stability of forced waves in a shifting environment


Authors: Jia-Bing Wang and Xiao-Qiang Zhao
Journal: Proc. Amer. Math. Soc. 147 (2019), 1467-1481
MSC (2010): Primary 35K57, 35R20, 92D25
DOI: https://doi.org/10.1090/proc/14235
Published electronically: December 31, 2018
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Abstract: This paper deals with the uniqueness and global stability of forced extinction waves for the nonlocal dispersal Fisher-KPP equation in a shifting environment where the favorable habitat is shrinking. Specifically, we first obtain the uniqueness by using the sliding technique and then establish the global exponential stability via the monotone semiflows approach combined with the method of super- and subsolutions. Our developed arguments can also be used to prove the same conclusion for the corresponding random diffusion problem.


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Additional Information

Jia-Bing Wang
Affiliation: School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, People’s Republic of China–and–Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada
Email: xbmwangjiabing@163.com

Xiao-Qiang Zhao
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada
Email: zhao@mun.ca

DOI: https://doi.org/10.1090/proc/14235
Keywords: Nonlocal Fisher-KPP equation, shifting environment, uniqueness of forced waves, global stability.
Received by editor(s): February 24, 2018
Received by editor(s) in revised form: May 13, 2018
Published electronically: December 31, 2018
Additional Notes: The first author was partially supported by the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) and the Joint Training Ph.D Program of China Scholarship Council (201606180060).
The second author was partially supported by the NSERC of Canada.
The second author is the corresponding author.
Communicated by: Wenxian Shen
Article copyright: © Copyright 2018 American Mathematical Society