BOUNDEDNESS FOR A NONLOCAL REACTION CHEMOTAXIS MODEL EVEN IN THE ATTRACTION-DOMINATED REGIME
This paper investigates a chemotaxis model with nonlinear diffusion and a nonlocal reaction source. It proves that, under specific conditions related to the diffusion, reaction, and growth coefficients, all solutions are uniformly bounded in time, regardless of the initial mass of the cell distribution. This suggests that even with small diffusion and strong initial mass, the nonlocal reaction term can prevent blow-up phenomena.