Asymptotic stability in a fully parabolic quasilinear chemotaxis model with general logistic source and signal production

2020 ◽  
Vol 268 (11) ◽  
pp. 6729-6777 ◽  
Author(s):  
Mengyao Ding ◽  
Wei Wang ◽  
Shulin Zhou ◽  
Sining Zheng
Keyword(s):  
Asymptotic Stability ◽  
Logistic Source ◽  
Chemotaxis Model ◽  
Signal Production

Qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source

2016 ◽  
Vol 09 (04) ◽  
pp. 1650051
Author(s):  
Haiyan Li ◽  
Jianguo Gao
Keyword(s):  
Fixed Point ◽  
Qualitative Analysis ◽  
Global Solution ◽  
Cell Mass ◽  
Logistic Source ◽  
Unique Global Solution ◽  
Chemotaxis Model ◽  
Initial Cell ◽  
Point Argument ◽  
Moser's Iteration

In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying a fixed point argument, [Formula: see text]-estimate technique and Moser’s iteration, we derive that the model admits a unique global solution provided the initial cell mass satisfying [Formula: see text] for [Formula: see text] While for [Formula: see text], there are no restrictions on the initial cell mass and the result still holds.

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