Boundedness in a quasilinear chemotaxis model with consumption of chemoattractant and logistic source

Abstract

This paper is devoted to the chemotaxis system with logistic sourceendowed with homogeneous Neumann boundary conditions and suitable initial conditions, where () is a bounded and smooth domain. Here we assume thatwhere , , and . Moreover, we will require for all with some , and . Then if one of the following cases hold:(i) , where(ii) ;(iii) and b is sufficiently large, it is proved that the system possesses a unique global bounded classical solution.