Emergence of lager densities in chemotaxis system with indirect signal production and non-radial symmetry case

Abstract

This paper deals with the classical solution of following chemotaxis system with indirect signal production, where χ, r, µ, d 1 , α, β, γ, λ > 0 and θ > 1, we find:(i) for ǫ ∈ (0, 1), d 2 > 0 and τ 1 = τ 2 = 0, if the initial data u 0 L θ (Ω) is sufficiently large, then for the associated solution of system and any positive constant M , one can find some points x, t such that u(x, t) > M.(0.1) (ii) for ǫ, τ 1 , τ 2 > 0, d 2 ≥ 0 and positive constant K, if F(u 0 , v 0 ) ≤ −K, here F is the Lyapunov functional to the system without damping source ru − µu θ , then (0.1