Finite-time blow-up in a degenerate chemotaxis system with flux limitation

This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by () { u t = ∇ ⋅ ( u ∇ u u 2 + | ∇ u | 2 ) − χ ∇ ⋅ ( u ∇ v 1 + | ∇ v | 2 ) , 0 = Δ v − μ + u , {equation} { } {cases} u_t=∇ · ( {u∇ u}{√u^2+|∇ u|^2} ) - χ \, ∇ · ( {u∇ v}{√1+|∇ v|^2} ), \\[3pt] 0=Δ v - μ + u, {cases}