Electron. J. Differential Equations

Electron. J. Differential Equations, Vol. 2025 (2025), No. 09, pp. 1-17.

Global boundedness in an indirect chemotaxis-consumption model with signal-dependent degenerate diffusion
Chun Wu

Abstract:
In this article, we consider the consumption chemotaxis system

\begin{matrix} u_{t} = Δ (u v^{α}) + a u - b u^{γ}, (x, t) \in Ω \times (0, \infty), \\ v_{t} = Δ v - u v w, (x, t) \in Ω \times (0, \infty), \\ w_{t} = - δ w + u, (x, t) \in Ω \times (0, \infty), \end{matrix}

on a smooth bounded domain

Ω \subset R^{n}

n \geq 2

with homogeneous Neumann boundary conditions, where

a > 0

b > 0

γ \geq 2

, and

δ > 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

	Chun Wu School of Mathematics Science Chongqing Normal University Chongqing 401331, China email: wuchun@cqnu.edu.cn

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Global boundedness in an indirect chemotaxis-consumption model with signal-dependent degenerate diffusion Chun Wu

Global boundedness in an indirect chemotaxis-consumption model with signal-dependent degenerate diffusion
Chun Wu