Boundedness and asymptotic stability in a chemotaxis model with indirect signal production and logistic source
| dc.contributor.author | Ye, Xiaobing | |
| dc.contributor.author | Wang, Liangchen | |
| dc.date.accessioned | 2023-04-25T18:00:32Z | |
| dc.date.available | 2023-04-25T18:00:32Z | |
| dc.date.issued | 2022-08-02 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16648 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | chemotaxis | |
| dc.subject | boundedness | |
| dc.subject | asymptotic behavior | |
| dc.subject | indirect signal production | |
| dc.title | Boundedness and asymptotic stability in a chemotaxis model with indirect signal production and logistic source | |
| dc.type | Article |