Chinese Quarterly Journal of Mathematics ›› 2022, Vol. 37 ›› Issue (1): 37-51.doi: 10.13371/j.cnki.chin.q.j.m.2022.01.004

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Stability of Traveling Wavefronts for a Spatially Nonlocal Population Model with Delay

  

  1. School of Mathematics and Physics, Lanzhou Jiaotong University
  • Received:2021-11-16 Online:2022-03-30 Published:2022-03-30
  • Contact: YANG Yun-rui (1979-), female, native of Tianshui, Gansu, professor of Lanzhou Jiaotong University, engages in nonlinear functional analysis, differential equations and dynamic systems; E-mail:lily1979101@163.com
  • About author:LIU Kai-kai (1994-), male, native of Ruzhou, Henan, postgraduate of Lanzhou Jiaotong University, engages in differential equations and dynamic systems; YANG Yun-rui (1979-), female, native of Tianshui, Gansu, professor of Lanzhou Jiaotong University, engages in nonlinear functional analysis, differential equations and dynamic systems; LI Xiao-wu (1997-), male, native of Fuyang, Anhui, postgraduate of Lanzhou Jiaotong University, engages in differential equations and dynamic systems.
  • Supported by:

    Supported by the NSF of China (Grant No. 11761046);

    Science and Technology Plan Foundation of Gansu Province of China (Grant No. 20JR5RA411);

    Foundation of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University.

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Abstract: The stability of traveling wavefronts for a spatially nonlocal population model with quasi-monotonicity and delay is discussed in this article. It is shown that all monostable wavefronts are exponentially stable for large speed with the help of weighted- energy method and comparison principle. The proper selection of the weighted function is necessary to overcome the difficulty caused by the nonlocal nonlinearity for establishing the energy estimates of solutions.

Key words: Stability, Wavefronts, Weighted-energy method

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