Global dynamics for an attraction-repulsion chemotaxis model with logistic source

In this paper, we investigate attraction-repulsion chemotaxis system with logistic source under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some L-P-estimate techniques, using different methods, we show that the system possesses global classical solution or at least one global weak solution. In addition to, we also consider large time behavior of solutions and steady solutions to an attraction-repulsion chemotaxis system. These results generalize and improve previously known ones, and partially results are new. (C) 2019 Elsevier Inc. All rights reserved.