Global Existence and Blow-Up for a Chemotaxis System

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....

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Main Authors: Xueyong Chen, Fuxing Hu, Jianhua Zhang, Jianwei Shen
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2017-03-01
Series:Mathematical Modelling and Analysis
Subjects:
chemotaxis
global existence
blow-up
numerical analysis
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/893
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spelling doaj-c2f10cee107d458dafd75d6e552f93632021-07-02T09:23:34ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102017-03-0122210.3846/13926292.2017.1292323Global Existence and Blow-Up for a Chemotaxis SystemXueyong Chen0Fuxing Hu1Jianhua Zhang2Jianwei Shen3School of Mathematics and Statistics, Xuchang University, Xuchang, ChinaDepartment of Mathematics, Huizhou University, Huizhou, ChinaSchool of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou, ChinaSchool of Mathematics and Statistics, Xuchang University, Xuchang, China 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. https://journals.vgtu.lt/index.php/MMA/article/view/893chemotaxisglobal existenceblow-upnumerical analysis
collection DOAJ
language English
format Article
sources DOAJ
author Xueyong Chen
Fuxing Hu
Jianhua Zhang
Jianwei Shen
spellingShingle Xueyong Chen
Fuxing Hu
Jianhua Zhang
Jianwei Shen
Global Existence and Blow-Up for a Chemotaxis System
Mathematical Modelling and Analysis
chemotaxis
global existence
blow-up
numerical analysis
author_facet Xueyong Chen
Fuxing Hu
Jianhua Zhang
Jianwei Shen
author_sort Xueyong Chen
title Global Existence and Blow-Up for a Chemotaxis System
title_short Global Existence and Blow-Up for a Chemotaxis System
title_full Global Existence and Blow-Up for a Chemotaxis System
title_fullStr Global Existence and Blow-Up for a Chemotaxis System
title_full_unstemmed Global Existence and Blow-Up for a Chemotaxis System
title_sort global existence and blow-up for a chemotaxis system
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2017-03-01
description 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.
topic chemotaxis
global existence
blow-up
numerical analysis
url https://journals.vgtu.lt/index.php/MMA/article/view/893
work_keys_str_mv AT xueyongchen globalexistenceandblowupforachemotaxissystem
AT fuxinghu globalexistenceandblowupforachemotaxissystem
AT jianhuazhang globalexistenceandblowupforachemotaxissystem
AT jianweishen globalexistenceandblowupforachemotaxissystem
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