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

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Author Info

  • 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))

Abstract

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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Bibliographic Info

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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Related research

Keywords: Parabolic partial differential equations; optimal control; infinite di- mensional problems; infinite time horizons; ill-posedness; dynamic programming;

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References

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  1. Carmen Camacho, 2013. "Spatial migration," Documents de travail du Centre d'Economie de la Sorbonne 13017, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2010. "Spatial dynamics and convergence: the spatial AK model," Working Papers 2010_06, Business School - Economics, University of Glasgow.
  3. 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.
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Cited by:
  1. Athanasios Yannacopoulos & Anastasios Xepapadeas & William Brock, . "Optimal Agglomerations in Dynamic Economics," DEOS Working Papers 1217, Athens University of Economics and Business.
  2. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," DEOS Working Papers 1402, Athens University of Economics and Business.

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