Blow-up phenomena in a parabolic–elliptic–elliptic attraction–repulsion chemotaxis system with superlinear logistic degradation. (November 2021) - Chiyo, Yutaro; Marras, Monica; Tanaka, Yuya; Yokota, Tomomi
Abstract: This paper is concerned with the attraction–repulsion chemotaxis system with superlinear logistic degradation, u t = Δ u − χ ∇ ⋅ ( u ∇ v ) + ξ ∇ ⋅ ( u ∇ w ) + λ u − μ u k, x ∈ Ω, t > 0, 0 = Δ v + α u − β v, x ∈ Ω, t > 0, 0 = Δ w + γ u − δ w, x ∈ Ω, t > 0, 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.