A logarithmic chemotaxis model featuring global existence and aggregation
The global existence of a chemotaxis model for cell aggregation phenomenon is obtained. The model system belongs to the class of logarithmic models and takes a Fokker–Planck type diffusion for the equation of cell density. We show that weak solutions exist globally in time in dimensions n∈{1,2,3} an...
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| Published in | Nonlinear analysis: real world applications Vol. 50; pp. 562 - 582 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Ltd
01.12.2019
Elsevier BV |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1468-1218 1878-5719 |
| DOI | 10.1016/j.nonrwa.2019.05.010 |
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| Abstract | The global existence of a chemotaxis model for cell aggregation phenomenon is obtained. The model system belongs to the class of logarithmic models and takes a Fokker–Planck type diffusion for the equation of cell density. We show that weak solutions exist globally in time in dimensions n∈{1,2,3} and for large initial data. The proof covers the parameter regimes that constant steady states are linearly stable. It also partially covers the other parameter regimes that constant steady states are unstable. We also find the sharp instability condition of constant steady states and provide numerical simulations which illustrate the formation of aggregation patterns. |
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| AbstractList | The global existence of a chemotaxis model for cell aggregation phenomenon is obtained. The model system belongs to the class of logarithmic models and takes a Fokker–Planck type diffusion for the equation of cell density. We show that weak solutions exist globally in time in dimensions n∈{1,2,3} and for large initial data. The proof covers the parameter regimes that constant steady states are linearly stable. It also partially covers the other parameter regimes that constant steady states are unstable. We also find the sharp instability condition of constant steady states and provide numerical simulations which illustrate the formation of aggregation patterns. |
| Author | Desvillettes, Laurent Trescases, Ariane Kim, Yong-Jung Yoon, Changwook |
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| Snippet | The global existence of a chemotaxis model for cell aggregation phenomenon is obtained. The model system belongs to the class of logarithmic models and takes a... |
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| SubjectTerms | Agglomeration Asymmetric diffusion Cell-aggregation Computer simulation Cross-diffusion Duality lemma Keller–Segel equations Mathematical models Parameters Pattern formation Stability Steady state |
| Title | A logarithmic chemotaxis model featuring global existence and aggregation |
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