In this paper, we consider a drift-diffusion model of parabolic-elliptic type, with three coupled equations. We prove that there exist parameter regimes for which non-simultaneous blow-up of solutions happens. This is in contrast to a two-chemotactic species model, coupled to an elliptic equation for an attractive chemical produced by the two species, where blow-up of one species implies blow-up of the other one at the same time. Also, we show that the range of parameters of the drift-diffusion model in this paper, for which blow-up happens, is larger than suggested by previous results in the literature.
"A Note on non-simultaneous blow-up for a drift-diffusion model." Differential Integral Equations 23 (5/6) 451 - 462, May/June 2010.