Global boundedness for a food chain model with general logistic source

This paper concerns the higher-dimensional food chain model with a general logistic source ut = Δu + u(1 − uα−1 − v − w), vt = Δv − ∇·(ξv∇u) + v(1 − vβ−1 + u − w), wt = Δw − ∇·(χw∇v) + w(1 − wγ−1 + v + u) in a smooth bounded domain Ω ⊂ Rn(n ≥ 2) with homogeneous Neumann boundary conditions. It is shown that for some conditions on the logistic degradation rates, this problem possesses a globally defined bounded classical solution.