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 inNonlinear analysis: real world applications Vol. 50; pp. 562 - 582
Main Authors Desvillettes, Laurent, Kim, Yong-Jung, Trescases, Ariane, Yoon, Changwook
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.12.2019
Elsevier BV
Subjects
Agglomeration
Asymmetric diffusion
Cell-aggregation
Computer simulation
Cross-diffusion
Duality lemma
Keller–Segel equations
Mathematical models
Parameters
Pattern formation
Stability
Steady state
Duality lemma
Pattern formation
Cross-diffusion
Asymmetric diffusion
Keller–Segel equations
Cell-aggregation
Online AccessGet full text
ISSN1468-1218
1878-5719
DOI10.1016/j.nonrwa.2019.05.010

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Summary: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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ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2019.05.010