Traveling bands for the Keller-Segel model with population growth
This paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical con...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.717 |
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| _version_ | 1832590123597824000 |
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| author | Shangbing Ai Zhian Wang |
| author_facet | Shangbing Ai Zhian Wang |
| author_sort | Shangbing Ai |
| collection | DOAJ |
| description | This paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical consumption rate for the existence of traveling wave solutions will change. Our results reveal that collective interaction of cell growth and chemical consumption rate plays an essential role in the generation of traveling bands. The research in the paper provides new insights into the mechanisms underlying the chemotactic pattern formation of wave bands. |
| format | Article |
| id | doaj-art-7089ab162f8c4eeaa2a53fb92545375d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7089ab162f8c4eeaa2a53fb92545375d2025-01-24T02:32:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-03-0112471773710.3934/mbe.2015.12.717Traveling bands for the Keller-Segel model with population growthShangbing Ai0Zhian Wang1Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong KongThis paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical consumption rate for the existence of traveling wave solutions will change. Our results reveal that collective interaction of cell growth and chemical consumption rate plays an essential role in the generation of traveling bands. The research in the paper provides new insights into the mechanisms underlying the chemotactic pattern formation of wave bands.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.717traveling wavesminimal wave speed.cell kineticskeller-segel modelchemotaxis |
| spellingShingle | Shangbing Ai Zhian Wang Traveling bands for the Keller-Segel model with population growth Mathematical Biosciences and Engineering traveling waves minimal wave speed. cell kinetics keller-segel model chemotaxis |
| title | Traveling bands for the Keller-Segel model with population growth |
| title_full | Traveling bands for the Keller-Segel model with population growth |
| title_fullStr | Traveling bands for the Keller-Segel model with population growth |
| title_full_unstemmed | Traveling bands for the Keller-Segel model with population growth |
| title_short | Traveling bands for the Keller-Segel model with population growth |
| title_sort | traveling bands for the keller segel model with population growth |
| topic | traveling waves minimal wave speed. cell kinetics keller-segel model chemotaxis |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.717 |
| work_keys_str_mv | AT shangbingai travelingbandsforthekellersegelmodelwithpopulationgrowth AT zhianwang travelingbandsforthekellersegelmodelwithpopulationgrowth |