Blow-up phenomena for a chemotaxis system with flux limitation

In this paper we consider nonnegative solutions of the following parabolic-elliptic cross-diffusion system [Formula presented] in Ω×(0,∞), with Ω a ball in RN, N≥3 under homogeneous Neumann boundary conditions and f(ξ)=(1+ξ)−α, [Formula presented], which describes gradient-dependent limitation of cross diffusion fluxes. Under conditions on f and initial data, we prove that a solution which blows up in finite time in L∞-norm, blows up also in Lp-norm for some p>1. Moreover, a lower bound of blow-up time is derived.