On the evolution of spatially distributed urban populations: Modelling and mathematical analysis

This paper deals with the construction and mathematical analysis of a new model for urban dynamics, which extends an initial one proposed by Y. Miyata and S. Yamaguchi in the context of a region of Japan. This new model includes spatial continuous structure and distinguishes two different time scales for the different processes taken into account: a slow one for the demography and a fast scale for the migration of individuals. Asymptotic behavior of solutions and stability of equilibria are established as a result of the combined action of demography and migration on population density and employment.