Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation
For a time-delayed reaction-diffusion equation of age-structuredsingle species population, the linear and nonlinear stability ofthe traveling wavefronts were proved by Gourley [4] andLi-Mei-Wong [8] respectively. The stability results,however, assume the delay-time is sufficiently small. We now prov...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2009-08-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.743 |
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| Summary: | For a time-delayed reaction-diffusion equation of age-structuredsingle species population, the linear and nonlinear stability ofthe traveling wavefronts were proved by Gourley [4] andLi-Mei-Wong [8] respectively. The stability results,however, assume the delay-time is sufficiently small. We now provethat the wavefronts remain stable even when the delay-time isarbitrarily large. This essentially improves the previousstability results obtained in [4, 8]. Finally, we point outthat this novel stability can be applied to the age-structuredreaction-diffusion equation with a more general maturation rate. |
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| ISSN: | 1551-0018 |