On explosions of solutions to a system of partial differential equations modelling chemotaxis - Jäger, Willi; Luckhaus, Stephan (Transactions of the American Mathematical Society, 1992)
A system of partial differential equations modelling chemotactic aggregation is analysed (Keller-Segel model). Conditions on the system of parameters are given implying global existence of smooth solutions. In two space dimensions and radially symmetric situations, explosion of the bacteria concentration in finite time is shown for a class of initial values.