Geodesic
Differentiation of a functional in the problem of parametric coefficient optimization in the global electric circuit equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1586-1601 
A. V. Chernov. Differentiation of a functional in the problem of parametric coefficient optimization in the global electric circuit equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1586-1601. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the problem of parametric optimization of the coefficient and the right-hand side of the linear global electric circuit equation, formulas for the first partial derivatives of an integral cost functional with respect to control parameters are obtained.

[1] Zhidkov A. A., Kalinin A. V., “Nekotorye voprosy matematicheskogo i chislennogo modelirovaniya globalnoi elektricheskoi tsepi v atmosfere”, Vestn. Nizhegorodskogo un-ta im. N.I. Lobachevskogo, 2009, no. 6(1), 150–158 | MR

[2] Sveshnikov A. G., Alshin A. B., Korpusov M. O., Nelineinyi funktsionalnyi analiz i ego prilozheniya k uravneniyam v chastnykh proizvodnykh, Nauchnyi mir, M., 2008

[3] Chernov A. V., “O differentsirovanii funktsionala v zadache parametricheskoi optimizatsii starshego koeffitsienta ellipticheskogo uravneniya”, Differents. ur-niya, 51:4 (2015), 538–547 | DOI | MR | Zbl

[4] Lubyshev F. V., Manapova A. R., “Raznostnye approksimatsii zadach optimizatsii dlya polulineinykh ellipticheskikh uravnenii v vypukloi oblasti s upravleniyami v koeffitsientakh pri starshikh proizvodnykh”, Zh. vychisl. matem. i matem. fiz., 53:1 (2013), 20–46 | DOI | MR | Zbl

[5] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973

[6] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978

[7] Iosida K., Funktsionalnyi analiz, LKI, M., 2007

[8] Hays P. B., Roble R. G., “A quasi-static model of global atmospheric electricity. 1. The lower atmosphere”, J. of Geophysical Research, 84:A7 (1979), 3291–3305 | DOI

[9] Hays P. B., Roble R. G., “A quasi-static model of global atmospheric electricity. 2. Electrical coupling between the upper and lower atmosphere”, J. of Geophysical Research, 84:A12 (1979), 7247–7256

[10] Dyuvo G., Lions Zh.-L., Neravenstva v mekhanike i fizike, Nauka, M., 1980, 384 pp.

[11] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, GITTL, M., 1956, 392 pp.

[12] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984, 752 pp.

[13] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989