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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AIMS Press
2009-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.743 |
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| author | Ming Mei Yau Shu Wong |
| author_facet | Ming Mei Yau Shu Wong |
| author_sort | Ming Mei |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-533916c77f4a4e8ab47747c0845341d4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-533916c77f4a4e8ab47747c0845341d42025-01-24T02:00:01ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-08-016474375210.3934/mbe.2009.6.743Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equationMing Mei0Yau Shu Wong1Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec, J4P 3P2Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec, J4P 3P2For 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.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.743travelingwavefrontstime-delayed reaction-diffusion equationexponential decay rate.nonlinear stability |
| spellingShingle | Ming Mei Yau Shu Wong Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation Mathematical Biosciences and Engineering travelingwavefronts time-delayed reaction-diffusion equation exponential decay rate. nonlinear stability |
| title | Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation |
| title_full | Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation |
| title_fullStr | Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation |
| title_full_unstemmed | Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation |
| title_short | Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation |
| title_sort | novel stability results for traveling wavefronts in an age structured reaction diffusion equation |
| topic | travelingwavefronts time-delayed reaction-diffusion equation exponential decay rate. nonlinear stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.743 |
| work_keys_str_mv | AT mingmei novelstabilityresultsfortravelingwavefrontsinanagestructuredreactiondiffusionequation AT yaushuwong novelstabilityresultsfortravelingwavefrontsinanagestructuredreactiondiffusionequation |