Property of the large densities in a two-species and two-stimuli chemotaxis system with competitive kinetics (Q2661205)

The authors consider a system of four parabolic equations describing interaction of two species via chemotactic influence of two chemicals and reactive terms of competitive type. The initial-boundary value problem in balls of \({\mathbb R}^n\), \(n\ge 3\), is shown to possess solutions of unbounded densities for ``small'' initial data. Energy arguments are used. However, finite time blow-up phenomena have not been detected.