Global existence, uniform boundedness, and stabilization in a chemotaxis system with density-suppressed motility and nutrient consumption

Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics population cells interacting with chemoattractant nutrient. The former induces chemotactic bias in diffusive motion is accounted by density-suppressed motility. first established generic positive non-increasing motility functions vanishing at infinity. Growth conditions on function guaranteeing next identified. Finally, sublinearly decaying functions, convergence to spatially homogeneous steady state shown, an exponential rate consumption rates behaving linearly near zero.