Blow-up phenomena in a parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with superlinear logistic degradation

Abstract

This paper is concerned with the attraction-repulsion chemotaxis system with superlinear logistic degradation,under homogeneous Neumann boundary conditions, in a ball Ω ⊂ R n (n ≥ 3), with constant parameters λ ∈ R, k > 1, µ, χ, ξ, α, β, γ, δ > 0. Blow-up phenomena in the system have been well investigated in the case λ = µ = 0, whereas the attraction-repulsion chemotaxis system with logistic degradation has been not studied. Under the condition that k > 1 is close to 1, this paper ensures a solution which blows up in L ∞ -norm and L σ -norm with some σ > 1 for some nonnegative initial data. Moreover, a lower bound of blow-up time is derived.

Boundedness and finite-time blow-up in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system

“…where χ, ξ, α, β, γ, δ > 0. In the case f (u) = λu − µu κ (λ ∈ R, µ > 0, κ > 1), finite-time blow-up was recently proved in [5] via the method in [44] when κ is sufficiently closed to 1 and χα − ξγ > 0 holds. Moreover, some related works deriving boundedness can be found in [15,28,29,30,31]; showing finite-time blow-up can be cited in [21]; dealing with nonlinear diffusion and sensitivities can be referred in [6,23,25].…”