Geodesic
Optimality systems for degenerate distributed control problems
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 16 (2013), pp. 60-70 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Necessary and sufficient conditions are obtained for control problems with systems which is described by degenerate evolution equation with initial condition of Cauchy or Showalter. Abstract results are illustrated on example of the free surface equation for filtered fluid.
Keywords: optimal control, optimality system, distributed control system, degenerate evolution equation. 
@article{VCHGU_2013_16_a5,
     author = {M. V. Plekhanova},
     title = {Optimality systems for degenerate distributed control problems},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {60--70},
     year = {2013},
     number = {16},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2013_16_a5/}
}
TY  - JOUR
AU  - M. V. Plekhanova
TI  - Optimality systems for degenerate distributed control problems
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2013
SP  - 60
EP  - 70
IS  - 16
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2013_16_a5/
LA  - ru
ID  - VCHGU_2013_16_a5
ER  - 
%0 Journal Article
%A M. V. Plekhanova
%T Optimality systems for degenerate distributed control problems
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2013
%P 60-70
%N 16
%U http://geodesic.mathdoc.fr/item/VCHGU_2013_16_a5/
%G ru
%F VCHGU_2013_16_a5
M. V. Plekhanova. Optimality systems for degenerate distributed control problems. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 16 (2013), pp. 60-70. http://geodesic.mathdoc.fr/item/VCHGU_2013_16_a5/

[1] Zh.-L. Lions, Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972, 412 pp. | MR

[2] Lions, Zh.-L., Upravlenie singulyarnymi raspredelennymi sistemami, Nauka,, M., 1987, 456 pp. | MR

[3] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nauka, M., 1972, 480 pp. | MR

[4] A. V. Fursikov, Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauch. kn., Novosibirsk, 1999, 350 pp.

[5] M. V. Plekhanova, V. E. Fëdorov, “Zadacha optimalnogo upravleniya dlya odnogo klassa vyrozhdennykh uravnenii”, Izv. RAN. Teoriya i sistemy upravleniya, 2004, no. 5, 40–44 | MR

[6] M. V. Plekhanova, A. F. Islamova, “O razreshimosti zadach smeshannogo optimalnogo upravleniya lineinymi raspredelennymi sistemami, ne razreshennymi otnositelno proizvodnoi po vremeni”, Izv. vuzov. Matematika, 2011, no. 7, 37–47 | MR | Zbl

[7] M. V. Plekhanova, V. E. Fëdorov, “O suschestvovanii i edinstvennosti reshenii zadach optimalnogo upravleniya lineinymi raspredelennymi sistemami, ne razreshennymi otnositelno proizvodnoi po vremeni”, Izv. RAN. Ser. Mat., 75:2 (2011), 177–194 | DOI | MR | Zbl

[8] M. V. Plekhanova, A. F. Islamova, “Zadachi s zhestkim smeshannym upravleniem dlya linearizovannogo uravneniya Bussineska”, Differents. uravneniya, 48:4 (2012), 565–576 | Zbl

[9] M. V. Plekhanova, V. E. Fëdorov, “Kriterii optimalnosti v zadache upravleniya dlya lineinogo uravneniya sobolevskogo tipa”, Izv. RAN. Teoriya i sistemy upravleniya, 2007, no. 2, 37–44 | MR

[10] E. S. Dzektser, “Obobschenie uravneniya dvizheniya gruntovykh vod so svobodnoi poverkhnostyu”, Dokl. AN SSSR, 202:5 (1972), 1031–1033 | Zbl

[11] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003, 216 pp. | MR | Zbl

[12] V. E. Fëdorov, “Golomorfnye razreshayuschie polugruppy uravnenii sobolevskogo tipa v lokalno vypuklykh prostranstvakh”, Mat. sb., 195:8 (2004), 131–160 | DOI | Zbl