Global boundedness and asymptotic behavior of the solutions to an attraction–repulsion chemotaxis-growth system

2021 ◽  
pp. 1-23
Author(s):  
Yong Liu ◽  
Zhongping Li
Keyword(s):  
Asymptotic Behavior ◽  
Growth System ◽  
Global Boundedness

Global boundedness and asymptotic behavior in a quasilinear attraction–repulsion chemotaxis model with nonlinear signal production and logistic-type source

2020 ◽  
Vol 30 (13) ◽  
pp. 2619-2689
Author(s):  
Guoqiang Ren ◽  
Bin Liu
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Global Existence ◽  
Classical Solutions ◽  
Chemotaxis Model ◽  
Signal Production ◽  
Nonlinear Signal ◽  
Nonlinear Signal Production ◽  
Global Boundedness

In this work, we consider the quasilinear attraction–repulsion chemotaxis model with nonlinear signal production and logistic-type source. We present the global existence of classical solutions under appropriate regularity assumptions on the initial data. In addition, the asymptotic behavior of the solutions is studied, and our results generalize and improve some well-known results in the literature.

scholarly journals Boundedness and Asymptotic Behavior to a Chemotaxis System with Indirect Signal Generation and Singular Sensitivity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jie Wu ◽  
Li Zhao ◽  
Heping Pan
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Rates Of Convergence ◽  
Signal Generation ◽  
Heat Semigroup ◽  
Singular Sensitivity ◽  
Chemotaxis System ◽  
Global Boundedness

In this paper, we consider the following indirect signal generation and singular sensitivity n t = Δ n + χ ∇ ⋅ n / φ c ∇ c ,   x ∈ Ω , t > 0 , c t = Δ c − c + w ,   x ∈ Ω , t > 0 , w t = Δ w − w + n ,   x ∈ Ω , t > 0 , in a bounded domain Ω ⊂ R N N = 2 , 3 with smooth boundary ∂ Ω . Under the nonflux boundary conditions for n , c , and w , we first eliminate the singularity of φ c by using the Neumann heat semigroup and then establish the global boundedness and rates of convergence for solution.

Boundedness and asymptotic behavior in a fully parabolic chemotaxis-growth system with signal-dependent sensitivity

2016 ◽  
Vol 17 (3) ◽  
pp. 909-929 ◽  
Author(s):  
Pan Zheng ◽  
Chunlai Mu ◽  
Liangchen Wang ◽  
Ling Li
Keyword(s):  
Asymptotic Behavior ◽  
Growth System

CONVECTIVE INSTABILITY IN CRYSTAL GROWTH SYSTEM

2002 ◽  
Vol 12 (12) ◽  
pp. 187-221 ◽  
Author(s):  
Koichi Kakimoto ◽  
Nobuyuki Imaishi
Keyword(s):  
Crystal Growth ◽  
Convective Instability ◽  
Growth System
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