Pattern formation by advection-diffusion in new economic geography

Abstract

A new economic geography model is proposed in which the migration of mobile workers is proximate and perturbed by non-economic factors. The model consists of a tractable core-periphery model assuming a quasi-linear log utility function of consumers and an advection-diffusion equation governing the time evolution of a population distribution. The stability of a spatially homogeneous stationary solution and the large time behavior of solutions to the model on a one-dimensional periodic space are investigated. When the spatially homogeneous stationary solution is unstable, solutions starting around it are found to eventually form spatial patterns with several urban areas in which mobile workers agglomerate.