In this paper, we solve a Solow model in continuous time and space. We prove the existence of a solution to the problem and its convergence to a stationary solution. The simulations of various scenario in the last section of the paper illustrates the convergence issue
Camacho Pérez, M. d. C., & Zou, B. (2004). The Spatial Solow Model. Economics Bulletin, 18(2), 1-11. https://hdl.handle.net/2078.5/152155 (Original work published 2004)