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 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 optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum...

In this paper, we make use of the Sobolev space W exp.1,1 (R+, R exp.n) to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an...

We use two stage optimal control techniques to solve some adoption problems under embodied technical change. We first solve a benchmark problem without learning behavior. At the date of switching, the consumption level is shown to drop, as the relative price of capital goes down (obsolescence)....

A benchmark AK optimal growth model with maintenance expenditures and endogenous utilization of capital is considered within an explicit vin- tage capital framework. Scrapping is endogenous, and the model allows for a clean distinction between age and usage dependent capital deprecia- tion and...

A benchmark AK optimal growth model with maintenance expenditures and endogeneous utilization of capital is considered within an explicit vintage capital framework. Scrapping is endogenous, and the model allows for a clean distinction between age and usage dependent capital depreciation and...

The special functions are intensively used in mathematical physics to solve differential systems. We argue that their use should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa...

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on...

We study a trade-off between economic and environmental indicators using a two-stage optimal control setting where the player can switch to a cleaner technology, that is environmentally “efficient”, but economically less productive. We provide an analytical characterization of the solution...