Geodesic
Optimal control to solutions of the Showalter–Sidorov problem for a Sobolev type equation
The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 1, pp. 42-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The sufficient and necessary conditions for the existence of optimal control to solutions of the Showalter–Sidorov problem for the equation which models potencial distribution of electrical field in a semiconductor are found.
Mots-clés : Sobolev type equation
Keywords: optimal control, the Showalter–Sidorov problem, electrical field equation. 
@article{IIGUM_2010_3_1_a4,
     author = {N. A. Manakova and E. A. Bogonos},
     title = {Optimal control to solutions of the {Showalter{\textendash}Sidorov} problem for a {Sobolev} type equation},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {42--53},
     year = {2010},
     volume = {3},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a4/}
}
TY  - JOUR
AU  - N. A. Manakova
AU  - E. A. Bogonos
TI  - Optimal control to solutions of the Showalter–Sidorov problem for a Sobolev type equation
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2010
SP  - 42
EP  - 53
VL  - 3
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a4/
LA  - ru
ID  - IIGUM_2010_3_1_a4
ER  - 
%0 Journal Article
%A N. A. Manakova
%A E. A. Bogonos
%T Optimal control to solutions of the Showalter–Sidorov problem for a Sobolev type equation
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2010
%P 42-53
%V 3
%N 1
%U http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a4/
%G ru
%F IIGUM_2010_3_1_a4
N. A. Manakova; E. A. Bogonos. Optimal control to solutions of the Showalter–Sidorov problem for a Sobolev type equation. The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 1, pp. 42-53. http://geodesic.mathdoc.fr/item/IIGUM_2010_3_1_a4/

[1] S. A. Zagrebina, “O zadache Shouoltera–Sidorova”, Izv. vuzov. Matematika, 2007, no. 3, 22–28 | MR | Zbl

[2] A. A. Zamyshlyaeva, “Fazovye prostranstva odnogo klassa lineinykh uravnenii sobolevskogo tipa vtorogo poryadka”, Vychisl. tekhnologii, 8:4 (2003), 45–54 | Zbl

[3] A. V. Keller, “Chislennoe reshenie zadachi startovogo upravleniya dlya sistemy uravnenii leontevskogo tipa”, Obozrenie priklad. i prom. matematiki, 16:2 (2009), 345–346

[4] M. O. Korpusov, A. G. Sveshnikov, “O «razrushenii» resheniya silno nelineinogo uravneniya psevdoparabolicheskogo tipa s dvoinoi nelineinostyu”, Mat. zametki, 79:6 (2006), 879–899 | DOI | MR | Zbl

[5] Zh.-L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR

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

[7] N. A. Manakova, “Zadacha optimalnogo upravleniya dlya uravneniya Oskolkova nelineinoi filtratsii”, Differents. uravneniya, 43:9 (2007), 1185–1192 | MR | Zbl

[8] Sveshnikov A. G., Alshin A. B., Korpusov M. O., Pletner Yu. D., Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007

[9] G. A. Sviridyuk, “Odna zadacha dlya obobschennogo filtratsionnogo uravneniya Bussineska”, Izv. vuzov. Matematika, 1990, no. 2, 55–61

[10] G. A. Sviridyuk, A. A. Efremov, “Optimalnoe upravlenie odnim klassom lineinykh vyrozhdennykh uravnenii”, DAN, 364:3 (1999), 323–325 | MR | Zbl

[11] G. A. Sviridyuk, N. A. Manakova, “Zadacha optimalnogo upravleniya dlya uravneniya Khoffa”, Sib. zhurn. industr. matematiki, 8:2 (2005), 144–151 | MR

[12] V. E. Fedorov, M. V. Plekhanova, “Optimalnoe upravlenie lineinymi uravneniyami sobolevskogo tipa”, Differents. uravneniya, 40:11 (2004), 1548–1556 | MR | Zbl

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

[14] G. V. Demidenko, S. V. Uspenskii, Partial differential equations and systems not solvable with respect to the highest-order derivative, Marcel Dekker, Inc., N. Y.–Basel–Hong Kong, 2003 | MR | Zbl

[15] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev type equations and degenerate semigroups of operators, VSP, Utrecht–Boston, 2003 | MR | Zbl