Boundedness in a quasilinear chemotaxis model with consumption of chemoattractant and logistic source. Issue 5 (4th April 2018) - Wang, Liangchen; Mu, Chunlai; Hu, Xuegang; Zheng, Pan
Abstract : This paper is devoted to the chemotaxis system with logistic source endowed with homogeneous Neumann boundary conditions and suitable initial conditions, where ( ) is a bounded and smooth domain. Here we assume that where, , 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.