Logistic damping effect in chemotaxis models with density-suppressed motility

Abstract

This paper is concerned with a parabolic-elliptic chemotaxis model with density-suppressed motility and general logistic source in an $n$-dimensional smooth bounded domain with Neumann boundary conditions. Under the minimal conditions for the density-suppressed motility function, we explore how strong the logistic damping can warrant the global boundedness of solutions, and further establish the asymptotic behavior of solutions on top of the conditions.