loading page

Analysis of long-term solution of chemotactic model with indirect signal consumption in three-dimensional case
  • Qiaoling Hu Hu
Qiaoling Hu Hu
University of Electronic Science and Technology of China Library

Corresponding Author:[email protected]

Author Profile


In this paper, we consider the chemotaxis model u_t&=\Delta u-\nabla\cdot(u\nabla v),& \qquad x\in\Omega,\,t>0,v_t&=\Delta v-vw,& \qquad x\in\Omega,\,t>0,w_t&=-\delta w+u,& \qquad x\in\Omega,\,t>0,under homogeneous Neumann boundary conditions in a bounded and convex domain $\Om\subset \mathbb{R}^3$ with smooth boundary, where $\delta>0$ is a given parameter. It is shown that for arbitrarily large initial data, this problem admits at least one global weak solution for which there exists $T>0$ such that the solution $(u,v,w)$ is bounded and smooth in $\Om\times(T,\infty)$. Furthermore, it is asserted that such solutions approach spatially constant equilibria in the large time limit.
14 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
15 Feb 2021Submission Checks Completed
15 Feb 2021Assigned to Editor
20 Feb 2021Reviewer(s) Assigned
29 May 2021Review(s) Completed, Editorial Evaluation Pending
30 May 2021Editorial Decision: Revise Major
18 Aug 20211st Revision Received
18 Aug 2021Submission Checks Completed
18 Aug 2021Assigned to Editor
23 Aug 2021Reviewer(s) Assigned
28 Nov 2021Review(s) Completed, Editorial Evaluation Pending
04 Dec 2021Editorial Decision: Revise Major
16 Feb 20222nd Revision Received
17 Feb 2022Submission Checks Completed
17 Feb 2022Assigned to Editor
17 Feb 2022Reviewer(s) Assigned
17 May 2022Review(s) Completed, Editorial Evaluation Pending
18 May 2022Editorial Decision: Revise Major
08 Aug 20223rd Revision Received
09 Aug 2022Assigned to Editor
09 Aug 2022Submission Checks Completed
10 Aug 2022Reviewer(s) Assigned
30 Aug 2022Review(s) Completed, Editorial Evaluation Pending
31 Aug 2022Editorial Decision: Accept