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2009, 6(4): 743-752. doi: 10.3934/mbe.2009.6.743

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, Canada

Received  November 2008 Revised  July 2009 Published  September 2009

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. Mathematical Biosciences & Engineering, 2009, 6 (4) : 743-752. doi: 10.3934/mbe.2009.6.743
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