scholarly journals Global boundedness of classical solutions to a logistic chemotaxis system with singular sensitivity

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Xiangdong Zhao ◽  
Keyword(s):  
Classical Solutions ◽  
Singular Sensitivity ◽  
Chemotaxis System ◽  
Global Boundedness

scholarly journals Asymptotic profile of a two-dimensional Chemotaxis–Navier–Stokes system with singular sensitivity and logistic source

2021 ◽  
pp. 1-42
Author(s):  
Peter Y. H. Pang ◽  
Yifu Wang ◽  
Jingxue Yin
Keyword(s):  
Energy Functional ◽  
Functional Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Qualitative Properties ◽  
Asymptotic Profile ◽  
Dimensional Version ◽  
Singular Sensitivity ◽  
Chemotaxis System ◽  
Global Boundedness

This paper is concerned with a spatially two-dimensional version of a chemotaxis system with logistic cell proliferation and death, for a singular tactic response of standard logarithmic type, and with interaction with a surrounding incompressible fluid through transport and buoyancy. Systems of this form are of significant relevance to the understanding of chemotaxis-fluid interaction, but the rigorous knowledge of their qualitative properties is yet far from complete. In this direction, using the conditional energy functional method, the present work provides some interesting contributions by establishing results on global boundedness, and especially on large time stabilization toward homogeneous equilibria, under mild assumptions on the initial data and appropriate conditions on the strength of the damping death effects.

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.

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