Global boundedness and stabilization for a three-component reaction-diffusion model with dual-dependent motility

In this paper, we consider the initial-boundary value problem of a three-component reaction-diffusion system with dual-dependent motility, which depends on both the chemical concentration and the nutrient level. We systematically establish the global existence, boundedness, and asymptotic behavior of the classical solutions to the system with no-flux boundary conditions through classified discussion and by exploiting specific structural properties of the motility function. In turn, by comparing the results obtained in the distinct cases, we demonstrate that the solution converges to different constant steady states, thereby indicating the crucial role of the dual-dependent motility function in the long-term behavior of the system.