Novel stability results for traveling  wavefronts in  an age-structured
     reaction-diffusion equation

Ming Mei; Yau Shu Wong; Ming Mei; Yau Shu Wong

doi:10.3934/mbe.2009.6.743

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

Ming Mei ,
Yau Shu Wong

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.
- 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[J]. Mathematical Biosciences and Engineering, 2009, 6(4): 743-752. doi: 10.3934/mbe.2009.6.743

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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.
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