Global existence and boundedness of a chemotaxis model with indirect production and general kinetic function

2020 ◽  
Vol 71 (4) ◽  
Author(s):  
Xie Li
Keyword(s):  
Global Existence ◽  
Chemotaxis Model ◽  
Kinetic Function

scholarly journals GLOBAL EXISTENCE AND BLOW-UP FOR A CHEMOTAXIS SYSTEM

2017 ◽  
Vol 22 (2) ◽  
pp. 237-251
Author(s):  
Xueyong Chen ◽  
Fuxing Hu ◽  
Jianhua Zhang ◽  
Jianwei Shen
Keyword(s):  
Global Existence ◽  
Parabolic System ◽  
Blow Up ◽  
Numerical Test ◽  
Growth Conditions ◽  
Chemotaxis Model ◽  
Global Strong Solution ◽  
Flux Boundary Conditions ◽  
Power Frequency ◽  
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. 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.

A logarithmic chemotaxis model featuring global existence and aggregation

2019 ◽  
Vol 50 ◽  
pp. 562-582 ◽  
Author(s):  
Laurent Desvillettes ◽  
Yong-Jung Kim ◽  
Ariane Trescases ◽  
Changwook Yoon
Keyword(s):  
Global Existence ◽  
Chemotaxis Model

scholarly journals The Global Existence of Solutions in Time for a Chemotaxis Model with Two Chemicals

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian Xu ◽  
Xiaolin Liu ◽  
Li Zhang
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Uniform Boundedness ◽  
Chemotaxis Model ◽  
Global Existence Of Solutions

This paper concerns the uniform boundedness and global existence of solutions in time for the chemotaxis model with two chemicals. We prove the system has global existence of solutions in time for any dimensionn.

scholarly journals Global Existence to an Attraction-Repulsion Chemotaxis Model with Fast Diffusion and Nonlinear Source

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yingjie Zhu ◽  
Fuzhong Cong
Keyword(s):  
Global Existence ◽  
Cell Density ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Energy Estimates ◽  
Fast Diffusion ◽  
Chemotaxis Model ◽  
Nonlinear Source ◽  
Strongly Coupled ◽  
Global Existence Of Solutions

This paper deals with the global existence of solutions to a strongly coupled parabolic-parabolic system of chemotaxis arising from the theory of reinforced random walks. More specifically, we investigate the attraction-repulsion chemotaxis model with fast diffusive term and nonlinear source subject to the Neumann boundary conditions. Such fast diffusion guarantees the global existence of solutions for any given initial value in a bounded domain. Our main results are based on the method of energy estimates, where the key estimates are obtained by a technique originating from Moser’s iterations. Moreover, we notice that the cell density goes to the maximum value when the diffusion coefficient of the cell density tends to infinity.

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