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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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
Online AccessGet full text
ISSN1392-6292
1648-3510
DOI10.3846/13926292.2017.1292323

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Abstract 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.
AbstractList 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.
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.Keywords: chemotaxis, global existence, blow-up, numerical analysis.AMS Subject Classification: 35K55; 35Q80.
Audience Academic
Author Shen, Jianwei
Zhang, Jianhua
Chen, Xueyong
Hu, Fuxing
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SubjectTerms blow-up
Boundary conditions
Chemotaxis
Existence theorems
global existence
Mathematical analysis
Mathematical models
numerical analysis
Reaction kinetics
Thresholds
Title Global Existence and Blow-Up for a Chemotaxis System
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