Persistence property in a two-species chemotaxis system with two signals

Abstract

This paper deals with a two-species chemotaxis system with two different signals under homogeneous Neumann boundary conditions in a bounded convex domain with the non-negative initial data. This system is a generalization of the classical Keller-Segel chemotaxis models to the case of two species which are attracted by two different chemical signals. Under suitable conditions, it is proved that for any non-negative global classical solutions, the masses of two species do not extinct at any time.