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On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics
Serdica Mathematical Journal, Tome 39 (2013) no. 3-4, pp. 331-354 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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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. 2010 Mathematics Subject Classification: 91B62, 91B72, 49K20, 49L20.
Keywords: Parabolic partial differential equations, optimal control, infinite dimensional problems, infinite time horizons, ill-posedness, dynamic programming 
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Boucekkine, R.; Camacho, C.; Fabbri, G. On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics. Serdica Mathematical Journal, Tome 39 (2013) no. 3-4, pp. 331-354. http://geodesic.mathdoc.fr/item/SMJ2_2013_39_3-4_a8/