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.

scholarly journals Blow-Up and Global Existence for a Degenerate Parabolic System with Nonlocal Sources

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Ling Zhengqiu ◽  
Wang Zejia
Keyword(s):  
Global Existence ◽  
Critical Exponent ◽  
Parabolic System ◽  
Blow Up ◽  
Nonnegative Solution ◽  
Degenerate Parabolic System ◽  
Nonlocal Sources ◽  
Nonnegative Solutions ◽  
Large Ball ◽  
Degenerate Parabolic

This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. By using the super- and subsolution techniques, the critical exponent of the system is determined. That is, ifPc=p1q1−(m−p2)(n−q2)<0, then every nonnegative solution is global, whereas ifPc>0, there are solutions that blowup and others that are global according to the size of initial valuesu0(x)andv0(x). WhenPc=0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain large enough that is, if it contains a sufficiently large ball, there is no global solution.

scholarly journals Blow-Up and Global Existence for a Quasilinear Parabolic System

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Chunchen Wu
Keyword(s):  
Global Existence ◽  
Parabolic System ◽  
Blow Up ◽  
Quasilinear Parabolic System ◽  
Quasilinear Parabolic

The problem of solutions to a class of quasilinear coupling parabolic system was studied. By constructing weak upper-solutions and weak lower-solutions, we obtain the global existence and blow-up of solutions under appropriate conditions.

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