School of Mathematics Science
Chongqing Normal University
Chongqing 401331, China
email: wuchun@cqnu.edu.cn
Chun Wu
Abstract:
In this article, we consider the consumption chemotaxis system
$$\displaylines{
u_t=\Delta(uv^\alpha)+au-bu^\gamma, \quad
(x,t)\in\Omega\times(0,\infty), \cr
v_t=\Delta{v}-uvw, \quad (x,t)\in\Omega\times(0,\infty),\cr
w_t=-\delta w+u, \quad (x,t)\in\Omega\times(0,\infty),
}$$
on a smooth bounded domain \(\Omega\subset \mathbb{R}^n\), \(n\geq 2\)
with homogeneous Neumann boundary conditions, where
\(a>0\), \(b>0\), \(\gamma\ge2\), and \(\delta>0\).
We shown that for sufficiently regular initial data, the
associated initial-boundary value problem possesses global bounded
classical solutions.
Submitted November 6, 2024. Published January 22, 2025.
Math Subject Classifications: 35K35, 35B40, 35A01, 92C17.
Key Words: Global boundedness; indirect chemotaxis-consumption; signal-dependent motility.
DOI: 10.58997/ejde.2025.09
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Chun Wu School of Mathematics Science Chongqing Normal University Chongqing 401331, China email: wuchun@cqnu.edu.cn |
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