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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:  October 31, 2008
Revised:  June 30, 2009
Published:  August 2009
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 35K57; Secondary: 34K20, 92D25.

    Citation:
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