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 u(t) = Delta + u(1 - u(alpha-1) - v - w), v(t) = Delta nu - del center dot (xi v del u) + v(1 - v(beta-1) + u - w), w(t) = Delta w - del center dot (chi w del v) + w(1 - w(gamma-1) + v + u) in a smooth bounded domain Omega subset of R-n (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. Published under an exclusive license by AIP Publishing.