Complete infinite-time mass aggregation in a quasilinear Keller–Segel system

Abstract

Radially symmetric global unbounded solutions of the chemotaxis system (Formula presented.) are considered in a ball Ω = BR(0) ⊂ ℝn, where n ≥ 3 and R > 0. Under the assumption that D and S suitably generalize the prototypes given by D(ξ) = (ξ + ι)m−1 and S(ξ) = (ξ + 1)−λ−1 for all ξ > 0 and some m ∈ ℝ, λ >0 and ι ≥ 0 fulfilling m+λ<1−2n, a considerably large set of initial data u0 is found to enforce a complete mass aggregation in infinite time in the sense that for any such u0, an associated Neumann type initial-boundary value problem admits a global classical solution (u, v) satisfying (Formula presented.) as well as (Formula presented.) with some C > 0.