Finite-time blow-up in a quasilinear fully parabolic attraction-repulsion chemotaxis system with density-dependent sensitivity

This article concerns the quasilinear fully parabolic attraction-repulsion chemotaxis system $${ u_t=∇ · ((u+1)ᵐ⁻¹∇ u -χ u(u+1)ᵖ⁻² ∇ v + ξ u(u+1)ᵖ⁻²∇ w), x ∈ Ω,\; t>0, v_t=Δ v+α u-β v, x ∈ Ω,\; t>0, w_t=Δ w+γ u-δ w, x ∈ Ω,\; t>0 }$$ with homogeneous Neumann boundary conditions, where \(Ω ⊂ R^n\) \((n ∈ \{2,3\})\) is an open ball, \(m, p ∈ R\), \(χ, ξ, α, β, γ, δ >0\) are constants. The main result asserts finite-time blow-up of solutions to this system with some positive initial data when \(χα-ξγ >0\), \(p ≥ 2\) and \(p-m>2/n\). For more information see https://ejde.math.txstate.edu/Volumes/2025/81/abstr.html