How strong a logistic damping can prevent blow-up for the minimal Keller–Segel chemotaxis system?
By Tian Xiang. 2016
119 citations recorded by the source corpus.
In this paper, we study the minimal Keller-Segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and other ingredient, especially, chemotactic aggregation to guarantee boundedness and convergence. More specifically, we establish how precisely strong a logistic source can prevent blow-up, and then we obtain an explicit relationship between logistic damping and other ingredient, especially, chemotactic aggregation so that convergences are ensured and their respective convergence rates are explicitly calculated out. Known results in the literature are completed and refined. Furthermore, our findings provide clues on how to produce blowup solutions for KS chemotaxis models with logistic sources.
Subfields: Genetics, Modeling and Simulation, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/54930a847fa6cb34e7d1eb42f781d024698d1609
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In Genetics
In Modeling and Simulation
- Michael Winkler
- Johannes Lankeit
- Tian Xiang
- Youshan Tao
- Xinru Cao
- Mario Fuest
- Tobias Black
- Giuseppe Viglialoro
In Molecular Biology
- Michael Winkler
- Johannes Lankeit
- Tian Xiang
- Youshan Tao
- Xinru Cao
- Giuseppe Viglialoro
- Mario Fuest
- Genglin Li
Citations in the corpus
- Attractiveness of Constant States in Logistic-Type Keller–Segel Systems Involving Subquadratic Growth Restrictions (2020, background): “Further findings in these directions, inter alia focusing at refinements with respect to parameter setting, or generalizations to slightly modified systems, or also qualitative facets such as wave-like behavior, can be found in [8], [14], [19], [18], [25], [49], [50], [55], [30], [31] and [32], for ”