Global existence of solutions to a two-species predator–prey parabolic chemotaxis system

Abstract

We consider the following two-species parabolic predator–prey chemotaxis system: [Formula: see text] under the homogeneous Neumann boundary conditions in a bounded domain [Formula: see text], [Formula: see text] with smooth boundary [Formula: see text]. We assume that the parameters [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are positive and the non-negative initial data [Formula: see text], where [Formula: see text] is the function of [Formula: see text] and defined as [Formula: see text] for some [Formula: see text] and all [Formula: see text]. Assume that there exists [Formula: see text] such that [Formula: see text] and let [Formula: see text], where [Formula: see text], then the system has a unique globally bounded classical solution [Formula: see text] in [Formula: see text].