Geodesic
On solving an inverse boundary problem for a parabolic equation by the quasi-revesibility method
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 6 (2012), pp. 8-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An inverse boundary problem for a parabolic equation is analyzed in the article. For the stable approximate solutions of the given problem the quasi-reversibility method is used. It consists in changing the original problem with a problem for hyperbolic equation with a small parameter. A sharp order error estimation of the method at one of the uniform regularization set is obtained.
Keywords: inverse problem; approximate method; error estimation. 
@article{VYURM_2012_6_a1,
     author = {E. V. Tabarintseva and L. D. Menikhes and A. D. Drozin},
     title = {On solving an inverse boundary problem for a parabolic equation by the quasi-revesibility method},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {8--13},
     year = {2012},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2012_6_a1/}
}
TY  - JOUR
AU  - E. V. Tabarintseva
AU  - L. D. Menikhes
AU  - A. D. Drozin
TI  - On solving an inverse boundary problem for a parabolic equation by the quasi-revesibility method
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2012
SP  - 8
EP  - 13
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VYURM_2012_6_a1/
LA  - ru
ID  - VYURM_2012_6_a1
ER  - 
%0 Journal Article
%A E. V. Tabarintseva
%A L. D. Menikhes
%A A. D. Drozin
%T On solving an inverse boundary problem for a parabolic equation by the quasi-revesibility method
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2012
%P 8-13
%N 6
%U http://geodesic.mathdoc.fr/item/VYURM_2012_6_a1/
%G ru
%F VYURM_2012_6_a1
E. V. Tabarintseva; L. D. Menikhes; A. D. Drozin. On solving an inverse boundary problem for a parabolic equation by the quasi-revesibility method. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 6 (2012), pp. 8-13. http://geodesic.mathdoc.fr/item/VYURM_2012_6_a1/

[1] Alifanov O. M., Artjukhin E. A., Rumjancev S. V., Extreme methods for solving incorrect problems, Nauka, M., 1988, 288 pp. (in Russ.) | MR | Zbl

[2] Tanana V. P., Tabarinceva E. V., “An approach to the approximation of discontinuous solutions of ill-posed problem”, Sibirskijj zhurnal industrial'nojj matematiki, 8:1(21) (2005), 130–142 (in Russ.) | Zbl

[3] Friedman A., Partial Differential Equations of Parabolic Type, Krieger Pub Co., 1983, 347 pp. ; т. 2, 304 с. | MR

[4] Beljaev N. M., Rjadno A. A., Methods of the theory of heat conduction, Studies manual for high schools in 2 parts, v. 1, Vysshaja shkola, M., 1982, 327 pp.; v. 2, 304 pp. (in Russ.)

[5] Lattes R., Lions J.-L., The Method of Quasi-reversibility, American Eisevier, New York, 1969, 388 pp. | MR | Zbl

[6] Samarskijj A. A., Vabishhevich P. N., Computational Heat Transfer, Editorial URSS, M., 2003, 782 pp. (in Russ.)

[7] Tabarinseva E. V., Kutuzov A. S., “A numerical method for solving the inverse problem of thermal diagnostics”, Nauka JuUrGU, v. 2, 2009, 161–164