A logarithmic chemotaxis model featuring global existence and aggregation

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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 is an element of {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. (C) 2019 Elsevier Ltd. All rights reserved.
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Issue Date
2019-12
Language
English
Article Type
Article
Citation

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v.50, pp.562 - 582

ISSN
1468-1218
DOI
10.1016/j.nonrwa.2019.05.010
URI
http://hdl.handle.net/10203/264321
Appears in Collection
MA-Journal Papers(저널논문)
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