Blow-up and decay criteria for a model of chemotaxis

For a system of equations introduced by Jäger and Luckhaus (1992) [6] as a model of chemotaxis, the questions of blow-up and global existence criteria are investigated. Specifically, for a convex region, a lower bound for the blow-up time is derived if the solution blows up, and explicit criteria to ensure non-blow-up are determined.