Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model
The paper is devoted to the study of a time-delayed reaction-diffusion equation of age-structured single species population. Linear stabilityfor this model was first presented by Gourley [4], when the time delay is small.Here, we extend the previous result to the nonlinear stability by using thetech...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2007-12-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.85 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590231014998016 |
|---|---|
| author | Guangrui Li Ming Mei Yau Shu Wong |
| author_facet | Guangrui Li Ming Mei Yau Shu Wong |
| author_sort | Guangrui Li |
| collection | DOAJ |
| description | The paper is devoted to the study of a time-delayed reaction-diffusion equation of age-structured single species population. Linear stabilityfor this model was first presented by Gourley [4], when the time delay is small.Here, we extend the previous result to the nonlinear stability by using thetechnical weighted-energy method, when the initial perturbation around thewavefront decays to zero exponentially as x→-∞, but the initial perturbationcan be arbitrarily large on other locations. The exponential convergent rate(in time) of the solution is obtained. Numerical simulations are carried out toconfirm the theoretical results, and the traveling wavefronts with a large delayterm in the model are reported. |
| format | Article |
| id | doaj-art-fa2c4285880b4acbb91f6482a592af07 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-fa2c4285880b4acbb91f6482a592af072025-01-24T01:57:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-12-01518510010.3934/mbe.2008.5.85Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population modelGuangrui Li0Ming Mei1Yau Shu Wong2Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1The paper is devoted to the study of a time-delayed reaction-diffusion equation of age-structured single species population. Linear stabilityfor this model was first presented by Gourley [4], when the time delay is small.Here, we extend the previous result to the nonlinear stability by using thetechnical weighted-energy method, when the initial perturbation around thewavefront decays to zero exponentially as x→-∞, but the initial perturbationcan be arbitrarily large on other locations. The exponential convergent rate(in time) of the solution is obtained. Numerical simulations are carried out toconfirm the theoretical results, and the traveling wavefronts with a large delayterm in the model are reported.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.85time-delayed reaction-diffusionequationexponentialdecay rate.traveling wavefrontsnon-linear stability |
| spellingShingle | Guangrui Li Ming Mei Yau Shu Wong Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model Mathematical Biosciences and Engineering time-delayed reaction-diffusionequation exponentialdecay rate. traveling wavefronts non-linear stability |
| title | Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model |
| title_full | Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model |
| title_fullStr | Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model |
| title_full_unstemmed | Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model |
| title_short | Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model |
| title_sort | nonlinear stability of traveling wavefronts in an age structured reaction diffusion population model |
| topic | time-delayed reaction-diffusionequation exponentialdecay rate. traveling wavefronts non-linear stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.85 |
| work_keys_str_mv | AT guangruili nonlinearstabilityoftravelingwavefrontsinanagestructuredreactiondiffusionpopulationmodel AT mingmei nonlinearstabilityoftravelingwavefrontsinanagestructuredreactiondiffusionpopulationmodel AT yaushuwong nonlinearstabilityoftravelingwavefrontsinanagestructuredreactiondiffusionpopulationmodel |