An integro-differential equation arising as a limit of individual cell-based models

In this paper, we study mathematical properties of an integro-differential equation that arises as a particular limit case in the study of individual cell-based model. We obtain global well-posedness for some classes of interaction potentials and finite time blow-up for others. The existence of space homogeneous steady states as well as long-time asymptotics for the solutions of the problem is also discussed.