Finite-time blow-up in the three-dimensional fully parabolic attraction-dominated attraction-repulsion chemotaxis system

Abstract

We show that the attraction-repulsion chemotaxis systemposed with homogeneous Neumann boundary conditions in bounded domains Ω = B R ⊂ R 3 , R > 0, admits radially symmetric solutions which blow-up in finite time if it is attractiondominated in the sense that χα − ξγ > 0.