Dynamic behavior analysis to a generalized chemotaxis-consumption system

In this paper, the following chemotaxis system with nonlinear consumption mechanisms is considered ut = Δu − χ∇ · (u∇v) + ξ∇ ·  (u∇w) + au − bum, vt = Δv − uαv, wt = Δw − uβw under homogeneous Neumann boundary conditions, where Ω⊂Rn(n≥2) is a smoothly bounded domain and parameters χ, ξ, a, b, α, β &...

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Bibliographic Details
Published in:Journal of mathematical physics 2024-01, Vol.65 (1)
Main Authors: Wang, Chang-Jian, Zheng, Zi-Han, Zhu, Xin-Cai
Format: Article
Language:English
Subjects:
Boundary conditions
Consumption
Convergence
Parameters
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Summary:In this paper, the following chemotaxis system with nonlinear consumption mechanisms is considered ut = Δu − χ∇ · (u∇v) + ξ∇ ·  (u∇w) + au − bum, vt = Δv − uαv, wt = Δw − uβw under homogeneous Neumann boundary conditions, where Ω⊂Rn(n≥2) is a smoothly bounded domain and parameters χ, ξ, a, b, α, β > 0 and m > 1. If m and l = max{α, β} satisfy m>maxl(n+2)2,1, then the system possesses a global classical solution, which is bounded in Ω × (0, ∞). Furthermore, it has been shown that such solution exponentially converges to equilibrium ((ab)1m−1,0,0) as t → ∞, where convergence rate can be formally characterized by the parameters of the system.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0176530