Population dynamics in a spatial Solow model with a convex-concave production function

In this chapter the classical Solow model is extended, by considering spatial dependence of the physical capital and population dynamics, and by introducing a nonconcave production function. The physical capital and population evolution equations are governed by semilinear parabolic differential equations which describe their evolution over time and space. The convergence to a steady state according to different hypotheses on the production function is discussed. The analysis is focused on an S-shaped production function, which allows the existence of saddle points and poverty traps. The evolution of this system over time, and its convergence to the steady state is described mainly through numerical simulations