Geodesic
Asymptotic behavior of solutions to multiplicative control problems for elliptic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1607-1618 
R. V. Brizitskii; A. S. Savenkova. Asymptotic behavior of solutions to multiplicative control problems for elliptic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1607-1618. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a6/
@article{ZVMMF_2008_48_9_a6,
     author = {R. V. Brizitskii and A. S. Savenkova},
     title = {Asymptotic behavior of solutions to multiplicative control problems for elliptic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1607--1618},
     year = {2008},
     volume = {48},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a6/}
}
TY  - JOUR
AU  - R. V. Brizitskii
AU  - A. S. Savenkova
TI  - Asymptotic behavior of solutions to multiplicative control problems for elliptic equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 1607
EP  - 1618
VL  - 48
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a6/
LA  - ru
ID  - ZVMMF_2008_48_9_a6
ER  - 
%0 Journal Article
%A R. V. Brizitskii
%A A. S. Savenkova
%T Asymptotic behavior of solutions to multiplicative control problems for elliptic equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 1607-1618
%V 48
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a6/
%G ru
%F ZVMMF_2008_48_9_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

The problems of optimal multiplicative control for the Helmholtz equation and the diffusion equation are studied. The control function is included multiplicatively in a mixed-type boundary condition specified on the entire domain boundary or its part. For each of the models under study, an iterative method for determining an approximate solution is constructed and theoretically substantiated for sufficiently large values of the regularization parameter.

[1] Savenkova A. C., “Multiplikativnoe upravlenie v zadache rasseyaniya dlya uravneniya Gelmgoltsa”, Sibirskii zhurnal industr. matem., 10:1 (2007), 128–139 | MR

[2] Alekseev G. V., “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplovoi konvektsii”, Vestn. NGU. Ser. matem., mekhan. i informatika, 6:2 (2006), 6–32

[3] Alekseev G. V., “Koeffitsientnye obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplo-massoperenosa”, Zh. vychisl. matem. i matem. fiz., 47:6 (2007), 1055–1076

[4] Illarionov A. A., “Asimptotika reshenii zadachi optimalnogo upravleniya dlya statsionarnykh uravnenii Nave–Stoksa”, Zh. vychisl. matem. i matem. fiz., 40:7 (2000), 1061–1070 | MR | Zbl

[5] Illarionov A. A., “Ob asimptotike reshenii zadachi optimalnogo upravleniya dlya statsionarnykh uravnenii Nave–Stoksa”, Zh. vychisl. matem. i matem. fiz., 41:7 (2001), 1045–1056 | MR | Zbl

[6] Savenkova A. C., “Asimptotika optimalnogo upravleniya v zadache rasseyaniya garmonicheskikh voln na prepyatstvii”, Zh. vychisl. matem. i matem. fiz., 47:9 (2007), 1602–1608 | MR

[7] Kolton D., Kress R., Metody integralnykh uravnenii v teorii rasseyaniya, Mir, M., 1987 | MR

[8] Sea Zh., Optimizatsiya. Teoriya i algoritmy, Mir, M., 1973