Large time behavior in a chemotaxis model with logistic growth and indirect signal production (Q2286666)

A system of three parabolic equations with chemotactic transport term, indirect signal production, and the logistic growth term \(\mu(u-u^\alpha)\) is studied in bounded domains of \({\mathbb R}^n\), \(n\ge 2\). If \(\alpha>\frac{n}{4}+\frac{1}{2}\) then solutions are global in time and uniformly bounded. Moreover, if \(\mu\) is large the solutions converge to the homogeneous steady state.