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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniqueness and global stability of forced waves in a shifting environment
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by Jia-Bing Wang and Xiao-Qiang Zhao PDF
Proc. Amer. Math. Soc. 147 (2019), 1467-1481 Request permission

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
  • MR Author ID: 1108250
  • Email: xbmwangjiabing@163.com
  • Xiao-Qiang Zhao
  • Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada
  • MR Author ID: 241619
  • Email: zhao@mun.ca
  • 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
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 1467-1481
  • MSC (2010): Primary 35K57, 35R20, 92D25
  • DOI: https://doi.org/10.1090/proc/14235
  • MathSciNet review: 3910413