We review an emerging application field to parabolic partial differential equations (PDEs), that's economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular,...

We study the existence of equilibrium and rational bubbles in a Ramsey model with heterogeneous agents, borrowing constraints and endogenous labor. Applying a nonstandard fixed-point theorem by Gale and Mas-Colell’s (1975), we prove the existence of equilibrium in a time-truncated bounded...

We investigate the effects of collaterals and monetary policy on growth rate dynamics in a Ramsey economy where agents have heterogeneous discount factors. We focus on the existence of business-cycle fluctuations based on self-fulfilling prophecies and on the occurrence of deterministic cycles...