Global solvability in a Keller-Segel-growth system with indirect signal production

In this paper, we consider a fully parabolic Keller-Segel-growth system with indirect signal production: u(t) = Delta u - chi del center dot(u del v) + f (u); v(t) = Delta v - v + w; w(t) = Delta w - w + u, x is an element of Omega, t > 0 in a bounded and smooth domain Omega subset of R-N (N >= 2) with no-flux boundary conditions, where chi is a positive constant. We present the global existence of generalized solutions under appropriate regularity assumptions on the initial data. In addition, the asymptotic behavior of generalized solutions is discussed, and our result generalize previously known ones.