Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/3443

 Title: On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics Authors: Boucekkine, R.Camacho, C.Fabbri, G. Keywords: Parabolic partial differential equationsoptimal controlinfinite dimensional problemsinfinite time horizonsill-posednessdynamic programming Issue Date: 2013 Publisher: Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 39, No 3-4, (2013), 331p-354p 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. 2010 Mathematics Subject Classification: 91B62, 91B72, 49K20, 49L20. URI: http://hdl.handle.net/10525/3443 ISSN: 1310-6600 Appears in Collections: Volume 39, Number 3-4

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