Global boundedness and asymptotic behavior of the solutions to an attraction–repulsion chemotaxis-growth system

Abstract

This paper deals with the following attraction–repulsion chemotaxis system with logistic source under homogeneous Neumann boundary conditions in a bounded domain with smooth boundary, where are assumed to be positive constants and with and . It is shown that the system admits a unique globally bounded classical solution provided that space dimension n = 2, or and , or and with some . Furthermore, under the additional assumption μ is suitably large, we show that the global classical solution will converge to the constant steady state exponentially as . Our results imply that the logistic source plays an important role on the behavior of the solutions in this model.