Blow-up in a degenerate attraction-repulsion chemotaxis system with flux limitation

Abstract In this paper we consider radially symmetric solutions of the cross-diffusion system with flux limitation, $$\begin{aligned} \left\{ \begin{array}{l} \begin{aligned} & u_t = \nabla \cdot \Big ( \frac{ u \nabla u }{\sqrt{u^2+ |\nabla u|^2}} \Big ) - \nabla \cdot \Big ( \frac{u \nabla (\chi v - \xi w)}{(1+ |\nabla v|^{2} + |\nabla w|^{2})^{q}} \Big ), \\ & 0= \Delta v +\alpha u - \beta v, \\ & 0=\Delta w +\gamma u - \delta w \end{aligned} \end{array} \right. \end{aligned}$$ u t = ∇ · ( u ∇ u u 2 + | ∇ u | 2 ) - ∇ · ( u ∇ ( χ v - ξ w ) ( 1 + | ∇ v | 2 + | ∇ w | 2 ) q ) , 0 = Δ v + α u - β v ,