Global Existence and Blow-Up for a Chemotaxis System

In this paper we consider a Keller-Segel-type chemotaxis model with reaction term under no-flux boundary conditions, where the kinetics term of the system is power function. Assuming some growth conditions, the existence of bounded global strong solution to the parabolic-parabolic system is given. W...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 22; no. 2; pp. 237 - 251
Main Authors Chen, Xueyong, Hu, Fuxing, Zhang, Jianhua, Shen, Jianwei
Format Journal Article
LanguageEnglish
Published Taylor & Francis 04.03.2017
Vilnius Gediminas Technical University
Subjects
blow-up
Boundary conditions
Chemotaxis
Existence theorems
global existence
Mathematical analysis
Mathematical models
numerical analysis
Reaction kinetics
Thresholds
global existence
blow-up
numerical analysis
chemotaxis
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Summary:In this paper we consider a Keller-Segel-type chemotaxis model with reaction term under no-flux boundary conditions, where the kinetics term of the system is power function. Assuming some growth conditions, the existence of bounded global strong solution to the parabolic-parabolic system is given. We also give the numerical test and find out that there exists a threshold. When the power frequency greater than the threshold, both global solution and blow-up solution exist.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1392-6292
1648-3510
DOI:10.3846/13926292.2017.1292323