  We consider a nonlinear, strongly coupled, parabolic system arising in the
modeling of burglary in residential areas. The system is of chemotaxis-type and
involves a logarithmic sensivity function and specific interaction and
relaxation terms. Under suitable assumptions on the data of the problem, we
give a rigorous proof of the existence of a global and bounded, classical
solution, thereby solving a problem left open in previous work on this model.
Our proofs are based on the construction of approximate entropies and on the
use of various functional inequalities. We also provide explicit numerical
conditions for global existence when the domain in a square, including concrete
cases involving values of the parameters which are expected to be physically
relevant
