Norm behaviour of solutions to a parabolic–elliptic system modelling chemotaxis in a domain of ℝ3

In this paper, we study a parabolic–elliptic system defined on a bounded domain of ?³, which comes from a chemotactic model. We first prove the existence and uniqueness of local in time solution to this problem in the Sobolev spaces framework, then we study the norm behaviour of solution, which may help us to determine the blow‐up norm of the maximal solution. Copyright © 2004 John Wiley & Sons, Ltd.