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On spatial-temporal dynamics of a Fisher-KPP equation with a shifting environment


Authors: Haijun Hu, Taishan Yi and Xingfu Zou
Journal: Proc. Amer. Math. Soc. 148 (2020), 213-221
MSC (2010): Primary 34C05, 34D20; Secondary 35B40, 92D25
DOI: https://doi.org/10.1090/proc/14659
Published electronically: July 8, 2019
MathSciNet review: 4042844
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Abstract: We consider a generalized Fisher-KPP equation with the growth function being time and space dependent in the form of ``shifting with constant speed''. The main concerns are extinction and persistence, as well as spatial-temporal dynamics. By employing a new method relating to semigroup and some subtle estimates, we not only extend the main results in Li et al. [SIAM J. Appl. Math. 74 (2014), pp. 1397-1417] to a scenario when the growth function may have no sign change, but also improve the main results there by dropping some restrictions on the initial functions.


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Haijun Hu
Affiliation: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, People’s Republic of China; and Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, Hunan 410114, People’s Republic of China
Email: huhaijun2000@163.com

Taishan Yi
Affiliation: School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai, Guangdong, 519082, People’s Republic of China
Email: yitaishan@mail.sysu.edu.cn

Xingfu Zou
Affiliation: Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada
Email: xzou@uwo.ca

DOI: https://doi.org/10.1090/proc/14659
Keywords: Reaction-diffusion equation, shifting environment, extinction, persistence, spreading speed.
Received by editor(s): December 3, 2018
Received by editor(s) in revised form: March 27, 2019, and April 9, 2019
Published electronically: July 8, 2019
Additional Notes: The first author was partially supported by NNSF of China (No. 11401051) and the Scientific Research Fund of Hunan Provincial Education Department (No. 18B152).
The second author was partially supported by NNSF of China (No. 11571371).
The third author was partially supported by NSERC of Canada (No. RGPIN-2016-04665).
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society