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Mathematical Biosciences and Engineering

2009, Volume 6, Issue 4: 743-752. doi: 10.3934/mbe.2009.6.743
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Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation

  • 1.
    Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec, J4P 3P2
  • 2.
    Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1
  • Received: 01 November 2008 Accepted: 29 June 2018 Published: 01 September 2009

  • MSC : Primary: 35K57; Secondary: 34K20, 92D25.

  • For a time-delayed reaction-diffusion equation of age-structured single species population, the linear and nonlinear stability of the traveling wavefronts were proved by Gourley [4] and Li-Mei-Wong [8] respectively. The stability results, however, assume the delay-time is sufficiently small. We now prove that the wavefronts remain stable even when the delay-time is arbitrarily large. This essentially improves the previous stability results obtained in [4, 8]. Finally, we point out that this novel stability can be applied to the age-structured reaction-diffusion equation with a more general maturation rate.

    Citation: Ming Mei, Yau Shu Wong. Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation[J]. Mathematical Biosciences and Engineering, 2009, 6(4): 743-752. doi: 10.3934/mbe.2009.6.743

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  • This article has been cited by:

    1. Guo-Bao Zhang, Global stability of traveling wave fronts for non-local delayed lattice differential equations, 2012, 13, 14681218, 1790, 10.1016/j.nonrwa.2011.12.010
    2. Jingwen Pei, Zhixian Yu, Huiling Zhou, Stability of Traveling Wavefronts for a Delayed Lattice System with Nonlocal Interaction, 2017, 21, 1027-5487, 10.11650/tjm/7964
    3. Guo-Bao Zhang, Wan-Tong Li, Nonlinear stability of traveling wavefronts in an age-structured population model with nonlocal dispersal and delay, 2013, 64, 0044-2275, 1643, 10.1007/s00033-013-0303-7
    4. Shangjiang Guo, Johannes Zimmer, Stability of travelling wavefronts in discrete reaction–diffusion equations with nonlocal delay effects, 2015, 28, 0951-7715, 463, 10.1088/0951-7715/28/2/463
    5. Shangjiang Guo, Patterns in a nonlocal time-delayed reaction–diffusion equation, 2018, 69, 0044-2275, 10.1007/s00033-017-0904-7
    6. Guo-Bao Zhang, Ruyun Ma, Spreading speeds and traveling waves for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity, 2014, 65, 0044-2275, 819, 10.1007/s00033-013-0353-x
    7. Ming Mei, Chunhua Ou, Xiao-Qiang Zhao, Global Stability of Monostable Traveling Waves For Nonlocal Time-Delayed Reaction-Diffusion Equations, 2010, 42, 0036-1410, 2762, 10.1137/090776342
    8. Rui Huang, Ming Mei, Yong Wang, Planar traveling waves for nonlocal dispersion equation with monostable nonlinearity, 2012, 32, 1078-0947, 3621, 10.3934/dcds.2012.32.3621
    9. Tianyuan Xu, Shanming Ji, Ming Mei, Jingxue Yin, Traveling waves for time-delayed reaction diffusion equations with degenerate diffusion, 2018, 265, 00220396, 4442, 10.1016/j.jde.2018.06.008
    10. Rui Huang, Ming Mei, Kaijun Zhang, Qifeng Zhang, Asymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations, 2015, 36, 1078-0947, 1331, 10.3934/dcds.2016.36.1331
    11. Changchun Liu, Ming Mei, Jiaqi Yang, Global stability of traveling waves for nonlocal time-delayed degenerate diffusion equation, 2022, 306, 00220396, 60, 10.1016/j.jde.2021.10.027
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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