Mathematical analysis demonstrates finite-time blow-up in degenerate chemotaxis models with flux limitation, highlighting critical thresholds governing singularity formation.
In this paper we consider radially symmetric solutions of the cross-diffusion system with flux limitation, $${aligned} \{ {array}{l} {aligned} & u_t = ∇ · ( { u ∇ u }{√u^2+ |∇ u|^2} ) - ∇ · ( {u ∇ (χ v - ξ w)}{(1+ |∇ v|² + |∇ w|²)q} ), \\ & 0= Δ v +α u - β v, \\ & 0=Δ w +γ u - δ w {aligned} {array} . {aligned}$$ 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 ,
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Marras et al. (2026) studied this question.
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