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

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. For more information see https://ejde.math.txstate.edu/Volumes/2025/09/abstr.html