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Article Dans Une Revue Serdica Mathematical Journal Année : 2013

On the optimal control of some parabolic partial differential equations arising in economics

Carmen Camacho
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Fabbri Giorgio

Résumé

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.
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Dates et versions

hal-00973388 , version 1 (04-04-2014)

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  • HAL Id : hal-00973388 , version 1

Citer

Raouf Boucekkine, Carmen Camacho, Fabbri Giorgio. On the optimal control of some parabolic partial differential equations arising in economics. Serdica Mathematical Journal, 2013, 39 (3), pp.331-354. ⟨hal-00973388⟩
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