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

Boucekkine, R., Camacho, C., and Fabbri, G.. "On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics." Serdica Mathematical Journal 39.3-4 (2013): 331-354. <http://eudml.org/doc/294993>.

@article{Boucekkine2013,
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.},
author = {Boucekkine, R., Camacho, C., Fabbri, G.},
journal = {Serdica Mathematical Journal},
keywords = {Parabolic partial differential equations; optimal control; infinite dimensional problems; infinite time horizons; ill-posedness; dynamic programming},
language = {eng},
number = {3-4},
pages = {331-354},
publisher = {Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences},
title = {On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics},
url = {http://eudml.org/doc/294993},
volume = {39},
year = {2013},
}

TY - JOUR
AU - Boucekkine, R.
AU - Camacho, C.
AU - Fabbri, G.
TI - On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics
JO - Serdica Mathematical Journal
PY - 2013
PB - Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
VL - 39
IS - 3-4
SP - 331
EP - 354
AB - 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.
LA - eng
KW - Parabolic partial differential equations; optimal control; infinite dimensional problems; infinite time horizons; ill-posedness; dynamic programming
UR - http://eudml.org/doc/294993
ER -