Abstract

In this paper the classical Solow model is extended, by consideringspatial dependence of the physical capital and population dynamics, andby introducing a nonconcave production function. The physical capitaland population evolution equations are governed by semilinear parabolicdifferential equations which describe their evolution over time and space.

The convergence to a steady state according to different hypotheses onthe production function is discussed. The analysis is focused on an S-shaped production function, which allows the existence of saddle pointsand poverty traps. The evolution of this system over time, and its con-vergence to the steady state is described mainly through numerical simulations.