Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 09, pp. 1-17.

Title: Global boundedness in an indirect chemotaxis-consumption model with signal-dependent degenerate diffusion

Author: Chun Wu (Chongqing Normal Univ., Chongqing, China)
  
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.