Emergence of large densities and simultaneous blow-up in a two-species chemotaxis system with competitive kinetics (Q2321049)

A system of three parabolic equations describing two competing species subject to chemotactic interactions is considered in bounded smooth domains of \(\mathbb{R}^n\), \(n\ge 3\), together with the homogeneous Neumann conditions. Using energy arguments, the author proves that if a blow-up occurs, then this happens simultaneously to both species.