  The nonlocal nonlinear aggregation equation in one space dimension is
investigated. In the so-called attractive case smooth solutions blow up in
finite time, so that weak measure solutions are introduced. The velocity
involved in the equation becomes discontinuous, and a particular care has to be
paid to its definition as well as the formulation of the corresponding flux.
When this is done, the notion of duality solutions allows to obtain global in
time existence and uniqueness for measure solutions. An upwind finite volume
scheme is also analyzed, and the convergence towards the unique solution is
proved. Numerical examples show the dynamics of the solutions after the blow up
time.
