A blow-up result for the chemotaxis system with nonlinear signal production and logistic source (Q2033585)

A parabolic-elliptic system of chemotaxis-growth is studied in balls in \({\mathbb R}^n\). The growth term is of logistic type \(g(u)=\lambda u-\mu u^\alpha\), and the production term is \(f(u)-\frac{1}{|\Omega|}\int_\Omega f(u(x,t))dx\) with a power-like function \(f\). The authors derive a sufficient condition for blowup of radially symmetric solutions with certain well concentrated initial data. This is a generalization and an extension of results known for systems with either growth terms only or nonlinear production term only.