The Urbanization Process with Moving Boundary

The paper proposes a dynamic model of urbanization in the regional system consisting of the central business district (CBD), the urban, and the rural areas. Processes of “eating up” the rural land by the residents and firms in the urban area are endogenously determined. Spatial and temporal land prices of the urban and rural areas are described by partial differential equations. The boundary between the urban and rural areas is temporarily moved by “eating-up” forces of the urban area. Movement of the boundary is determined by interactions between the urban and rural areas near the boundary. The model consists of three partial differential equations under appropriate boundary and initial conditions. It describes how the actual regional pattern is disturbed far away from the equilibrium by inflationary forces. An analytic solution of the fixed rural land price is given.