On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics

Raouf Boucekkine (), Carmen Camacho and Giorgio Fabbri

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: 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, the heuristic application of the maximum principle to the latter leads to single out a serious ill-posedness problem, which is, in our view, a barrier to the use of parabolic PDEs in economic growth studies as the latter are interested in long-run asymptotic solutions, thus requiring the solution to infinite time horizon optimal control problems. Adapted dynamic programming methods are used to dig deeper into the identified ill-posedness issue.

Keywords: optimal control; infinite dimensional problems; parabolic partial differential equations; infinite time horizons; ill-posedness; dynamic programming (search for similar items in EconPapers)
Date: 2013-06
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00831042
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Citations: View citations in EconPapers (22)

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Related works:
Working Paper: On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics (2013)
Working Paper: On the optimal control of some parabolic partial differential equations arising in economics (2013)
Working Paper: On the optimal control of some parabolic partial differential equations arising in economics (2013)
Working Paper: On the optimal control of some parabolic partial differential equations arising in economics (2013)
Working Paper: On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics (2013)
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