On a two-species chemotaxis system with indirect signal production and general competition terms

Abstract

This paper deals with a two-competing-species chemotaxis system with indirect signal production [Formula: see text] under homogeneous Neumann boundary conditions in a smoothly bounded domain [Formula: see text], with the nonnegative initial data [Formula: see text], where [Formula: see text] and [Formula: see text], [Formula: see text]. When [Formula: see text], we study the global existence and boundedness of classical solutions to the above system in a three-dimensional bounded domain under some suitable conditions of parameters. When [Formula: see text], [Formula: see text] [Formula: see text], we discuss the existence of globally bounded solution for all [Formula: see text] provided that the parameters satisfy some suitable assumptions. Furthermore, we consider the asymptotic stabilization of globally bounded solutions to the above system under weak competition and strongly asymmetric competition cases, respectively.