Large‐time behavior in a two‐species chemotaxis‐competition system with nonlocal nonlinear growth terms

Abstract This paper deals with a two‐species chemotaxis‐competition system in a setting that not only accounts for a class of nonlinear variants of the chemotactic cross‐diffusion processes, but also involves an external source describing a superlinear growth effect under nonlocal resource consumption. Apart from that, the considered chemoattractant is assumed to be produced according to a fairly general power law. We first confirm the global existence and boundedness of classical solutions to an associated Neumann initial‐boundary value problem under some appropriate parameter conditions. Moreover, it is shown that these global bounded solutions converge to the spatially homogeneous coexistence state as time tends to infinity.