Lower bounds for blow-up in a model of chemotaxis (Q641626)

Many special cases of the classical Keller-Segel system for modeling chemotaxis have been investigated in the literature, and typically the solution of the governing equations blows up at some finite time. In the paper under review, the authors derive a lower bound for the blow-up time in a parabolic-parabolic model in both \(\mathbb R^{2}\) and \(\mathbb R^{3}.\)