A degenerate attraction-repulsion chemotaxis system with logistic-type superlinear degradation

Marras, Monica

;Vernier-Piro, Stella;Yokota, Tomomi

2026-01-01

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Abstract

In this paper, we consider radially symmetric solutions of the degenerate cross-diffusion system with flux limitation diffusion and logistic source, (Formula presented) in Ω × (0, ∞), with Ω a ball in RN, N ≥ 1, and subjected to no-flux boundary conditions. The logistic dampening satisfies f(u) = λu−µuk with λ, µ positive constants and k ≥ 1. If N ≥ 3 and χα − ξγ > 0, under certain smallness conditions on logistic degradation, we demonstrate that the solution u(x, t) exhibits blow-up behavior in L∞-norm at a finite time. Moreover, for some p > N, we prove that the solution also blows up in Lp-norm. On the other hand, if χα − ξγ < 0, or if χα − ξγ > 0 and k is large, we prove that the solution is global in time