Global existence of bounded solutions for a quasilinear chemotaxis system with logistic source

Abstract

In this paper, we deal with the chemotaxis system with logistic source under homogeneous Neumann boundary conditions in a bounded convex domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by developing some Lp-estimate techniques, we show that the system possesses at least one global and bounded weak solution. Our results generalized and improved previous results, and partially results are new.