Blow-up phenomena in chemotaxis systems with a source term

This paper dealswith a parabolic-parabolic Keller-Segel-type systemin a bounded domain of R-N, {N = 2; 3}, under different boundary conditions, with time-dependent coefficients and a positive source term. The solutions may blowup in finite time t *: and under appropriate assumptions on data, explicit lower bounds for blow-up time are obtained when blow up occurs. Copyright (C) 2015 JohnWiley & Sons, Ltd.