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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

    ()
    (AMSE - Aix-Marseille School of Economics - Centre national de la recherche scientifique (CNRS) - École des Hautes Études en Sciences Sociales (EHESS) - Ecole Centrale Marseille (ECM), IRES-CORE - Université Catholique de Louvain)

  • Carmen Camacho

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Giorgio Fabbri

    ()
    (EPEE - Université d'Evry-Val d'Essonne)

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.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00831042.

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Date of creation: Jun 2013
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Handle: RePEc:hal:cesptp:halshs-00831042

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Related research

Keywords: parabolic partial differential equations; optimal control; infinite dimensional problems; infinite time horizons; ill-posedness; dynamic programming;

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  1. Carmen Camacho, 2013. "Spatial migration," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801109, HAL.
  2. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "Spatial dynamics and convergence: The spatial AK model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00827641, HAL.
  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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