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

J. El Ghordaf , Hassan Hbid (1) , E. Sanchez (2) , Michel Langlais (3, 4)

1 Department of Mathematics [Marroco]
2 MA - Departamento de Matemática Aplicada
3 IMB - Institut de Mathématiques de Bordeaux
4 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics

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.

Keywords: Monotone semiflows; Urban dynamics; Spatial structure

Domains: Analysis of PDEs [math.AP]

J. El Ghordaf, Hassan Hbid, E. Sanchez, Michel Langlais. On the evolution of spatially distributed urban populations: Modelling and mathematical analysis. Nonlinear Analysis: Real World Applications, 2009, 10, pp.2945-2960. ⟨10.1016/j.nonrwa.2008.09.013⟩. ⟨hal-00402160⟩