Travelling waves in hyperbolic chemotaxis equations
Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel,...
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| Fformat: | Journal article |
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2010
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| _version_ | 1826283509189181440 |
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| author | Xue, C Hwang, H Painter, K Erban, R |
| author_facet | Xue, C Hwang, H Painter, K Erban, R |
| author_sort | Xue, C |
| collection | OXFORD |
| description | Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. |
| first_indexed | 2024-03-07T00:59:56Z |
| format | Journal article |
| id | oxford-uuid:895f53d5-1b19-4789-be7e-e8a4ae3bba08 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:59:56Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:895f53d5-1b19-4789-be7e-e8a4ae3bba082022-03-26T22:24:08ZTravelling waves in hyperbolic chemotaxis equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:895f53d5-1b19-4789-be7e-e8a4ae3bba08Mathematical Institute - ePrints2010Xue, CHwang, HPainter, KErban, RMathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. |
| spellingShingle | Xue, C Hwang, H Painter, K Erban, R Travelling waves in hyperbolic chemotaxis equations |
| title | Travelling waves in hyperbolic chemotaxis equations |
| title_full | Travelling waves in hyperbolic chemotaxis equations |
| title_fullStr | Travelling waves in hyperbolic chemotaxis equations |
| title_full_unstemmed | Travelling waves in hyperbolic chemotaxis equations |
| title_short | Travelling waves in hyperbolic chemotaxis equations |
| title_sort | travelling waves in hyperbolic chemotaxis equations |
| work_keys_str_mv | AT xuec travellingwavesinhyperbolicchemotaxisequations AT hwangh travellingwavesinhyperbolicchemotaxisequations AT painterk travellingwavesinhyperbolicchemotaxisequations AT erbanr travellingwavesinhyperbolicchemotaxisequations |