Geodesic
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.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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 
@article{SMJ2_2013_39_3-4_a8,
     author = {Boucekkine, R. and Camacho, C. and Fabbri, G.},
     title = {On the {Optimal} {Control} of {Some} {Parabolic} {Partial} {Differential} {Equations} {Arising} in {Economics}},
     journal = {Serdica Mathematical Journal},
     pages = {331--354},
     publisher = {mathdoc},
     volume = {39},
     number = {3-4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2013_39_3-4_a8/}
}
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
SP  - 331
EP  - 354
VL  - 39
IS  - 3-4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2013_39_3-4_a8/
LA  - en
ID  - SMJ2_2013_39_3-4_a8
ER  - 
%0 Journal Article
%A Boucekkine, R.
%A Camacho, C.
%A Fabbri, G.
%T On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics
%J Serdica Mathematical Journal
%D 2013
%P 331-354
%V 39
%N 3-4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2013_39_3-4_a8/
%G en
%F SMJ2_2013_39_3-4_a8
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/