  We consider an initial-boundary value problem describing the formation of
colony patterns of bacteria Escherichia coli. This model consists of
reaction-diffusion equations coupled with the Keller-Segel system from the
chemotaxis theory in a bounded domain, supplemented with zero-flux boundary
conditions and with non-negative initial data. We answer questions on the
global in time existence of solutions as well as on their large time behaviour.
Moreover, we show that solutions of a related model may blow up in a finite
time.
