Boundedness and asymptotic stability in a chemotaxis model with indirect signal production and logistic source
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Date
2022-08-02
Authors
Ye, Xiaobing
Wang, Liangchen
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the chemotaxis-growth system with indirect signal production
ut = ∆u - ∇ ∙ (u∇v) + μu(1 - u), x ∈ Ω, t > 0,
0 = ∆v - v + w, x ∈ Ω, t > 0,
wt = -δw + u, x ∈ Ω, t > 0,
on a smooth bounded domain Ω ⊂ ℝn (n ≥ 1) with homogeneous Neumann boundary condition, where the parameters μ, δ > 0. It is proved that if n ≤ 2 and μ > 0, for all suitably regular initial data, this model possesses a unique global classical solution which is uniformly-in-time bounded. While in the case n ≥ 3, we show that if μ is sufficiently large, this system possesses a global bounded solution. Furthermore, the large time behavior and rates of convergence have also been considered under some explicit conditions.
Description
Keywords
chemotaxis, boundedness, asymptotic behavior, indirect signal production
Citation
Ye, X., & Wang, L. (2022). Boundedness and asymptotic stability in a chemotaxis model with indirect signal production and logistic source. <i>Electronic Journal of Differential Equations, 2022</i>(58), pp. 1-17.
Rights
Attribution 4.0 International