Mathematical Biosciences and Engineering, 2009, 6(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

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.
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Keywords traveling wavefronts; time-delayed reaction-diffusion equation; exponential decay rate.; nonlinear stability

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


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