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

We show that the attraction-repulsion chemotaxis system {u(t) = Delta(u) - chi del.(u del v(1)) + xi del.(v del v(2)) partial derivative(t)v(1) = Delta v(1) - beta v(1) + alpha u partial derivative(t)v(2) = Delta v(2) - delta v(2) + gamma u, posed with homogeneous Neumann boundary conditions in bounded domains Omega = B-R subset of R-3, R > 0, admits radially symmetric solutions which blow-up in finite time if it is attraction-dominated in the sense that chi alpha - xi gamma > 0. (C) 2021 Elsevier Inc. All rights reserved.