Finite time blow-up in a parabolic–elliptic Keller–Segel system with flux dependent chemotactic coefficient

A parabolic–elliptic Keller–Segel system u<inf>t</inf>=Δu−χ∇⋅(uf(|∇v|)∇v),0=Δv−M+u,with homogeneous Neumann boundary condition is considered in a radially symmetric domain Ω=B<inf>R</inf>(0)⊂R^N(N≥3), where [Formula presented] and B<inf>R</inf>(0) is a N-dimensional ball of radius R>0. We assert that under a condition on the initial data, radial weak solutions blow-up in finite time when [Formula presented]