About solving one boundary inverse problem for parabolic equation
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 3 (2010), pp. 21-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of restoration of boundary conditions of the third genre using additional information about decision of the parabolic equation is considered. The method of the approached solution of the set problem with a choice of parameter of regularization using M. M. Lavrenteva's scheme [1] and one of schemes of a posteriori choice of regularization parameter is considered. The exact in order estimation of error of the constructed approximate answer based on one of the classes of the uniform regularization is received.
Keywords: inverse problem, approximate answer method
Mots-clés : error estimation.
@article{VYURM_2010_3_a2,
     author = {E. V. Tabarintseva},
     title = {About solving one boundary inverse problem for parabolic equation},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {21--28},
     year = {2010},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2010_3_a2/}
}
TY  - JOUR
AU  - E. V. Tabarintseva
TI  - About solving one boundary inverse problem for parabolic equation
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2010
SP  - 21
EP  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VYURM_2010_3_a2/
LA  - ru
ID  - VYURM_2010_3_a2
ER  - 
%0 Journal Article
%A E. V. Tabarintseva
%T About solving one boundary inverse problem for parabolic equation
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2010
%P 21-28
%N 3
%U http://geodesic.mathdoc.fr/item/VYURM_2010_3_a2/
%G ru
%F VYURM_2010_3_a2
E. V. Tabarintseva. About solving one boundary inverse problem for parabolic equation. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 3 (2010), pp. 21-28. http://geodesic.mathdoc.fr/item/VYURM_2010_3_a2/

[1] M. M. Lavrentev, O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, Nauka, Novosibirsk, 1962, 92 pp. | MR

[2] V. P. Tanana, “Ob optimalnom po poryadku metode resheniya odnoi obratnoi zadachi dlya parabolicheskogo uravneniya”, Dokl. RAN, 407:3 (2006), 316–318 | MR

[3] A. M. Ilin, Uravneniya matematicheskoi fiziki, Izd-vo ChelGU, Chelyabinsk, 2005, 171 pp.

[4] V. K. Ivanov, I. V. Melnikova, A. I. Filinkov, Differentsialno-operatornye uravneniya i nekorrektnye zadachi, Nauka, M., 1995, 175 pp. | MR

[5] V. P. Tanana, E. V. Tabarintseva, “Ob odnom podkhode k priblizheniyu razryvnogo resheniya nekorrektno postavlennoi zadachi”, Sibirskii zhurnal industrialnoi matematiki, 8:1(21) (2005), 129–142 | MR

[6] V. S. Vladimirov, Uravneniya matematicheskoi fiziki, Nauka, M., 1971, 512 pp. | MR | Zbl

[7] S. Pereverzev, E. Schock, “On the adaptive selection of the parameter in regularization of ill-posed problems”, SIAM J. Numer. Anal., 43:5 (2005), 2060–2076 | DOI | MR | Zbl

[8] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989, 496 pp. | MR | Zbl

[9] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965, 588 pp. | MR

[10] Zh. Dedonne, Osnovy sovremennogo analiza, Mir, M., 1964, 430 pp. | MR