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

  • Raouf Boucekkine

    ()

    (Aix-Marseille University (Aix-Marseille School of Economics), EHESS and CNRS, France and IRES-CORE, UCLouvain, Belgium)

  • Carmen Camacho

    ()

    (CNRS, Université Paris I)

  • Giorgio Fabbri

    ()

    (EPEE, Université d’Evry-Val-d’Essonne (TEPP, FR-CNRS 3126))

We review an emerging application field to parabolic partial differential equa- tions (PDEs), that’s economic growth theory. After a short presentation of con- crete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular, the heuristic appli- cation 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 solu- tions, 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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File URL: http://epee.univ-evry.fr/RePEc/2013/13-10.pdf
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Paper provided by Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne in its series Documents de recherche with number 13-10.

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Length: 26 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:eve:wpaper:13-10
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  1. Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers Department of Economics 2004/14, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
  2. Raouf BOUCEKKINE & Carmen CAMACHO & Giorgio FABBRI, 2010. "Spatial dynamics and convergence: the spatial AK model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2010009, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. Carmen Camacho, 2013. "Spatial migration," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801109, HAL.
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