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

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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File URL: http://www.amse-aixmarseille.fr/sites/default/files/_dt/2012/wp_2013_-_nr_34.pdf
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Paper provided by Aix-Marseille School of Economics, Marseille, France in its series AMSE Working Papers with number 1334.

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Length: 26 pages
Date of creation: 05 Jun 2013
Date of revision: 05 Jun 2013
Handle: RePEc:aim:wpaimx:1334
Contact details of provider: Web page: http://www.amse-aixmarseille.fr/en

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  1. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
  2. 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.
  3. 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.
  4. 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.
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