Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimensions

∂u ∂ν = ∂v ∂ν = ∂w ∂ν = 0, x ∈ ∂Ω, t > 0, u(x, 0) = u0(x), v(x, 0) = v0(x), x ∈ Ω, in a bounded smooth but not necessarily convex domain Ω ⊂ R(n ≥ 2) with model parameters ξ1, ξ2, d, θ > 0, a, χ, μ ≥ 0. Based on subtle energy estimates, we first identify two positive constants ξ0 and μ0 such that the above problem allows only global classical solutions with qualitative bounds provided one of the following conditions holds: (1) ξ1 ≥ ξ0χ2; (2) θ = 1, μ ≥ max {