Geodesic
Identification of a dissipation coefficient by a variational method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1882-1893 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A generalized inverse problem for the identification of the absorption coefficient for a hyperbolic system is considered. The well-posedness of the problem is examined. It is proved that the regular part of the solution is an $L_2$ function, which reduces the inverse problem to minimizing the error functional. The gradient of the functional is determined in explicit form from the adjoint problem, and approximate formulas for its calculation are derived. A regularization algorithm for the solution of the inverse problem is considered. Numerical results obtained for various excitation sources are displayed. 
@article{ZVMMF_2006_46_10_a14,
     author = {A. V. Baev and N. V. Kutsenko},
     title = {Identification of a~dissipation coefficient by a~variational method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1882--1893},
     year = {2006},
     volume = {46},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a14/}
}
TY  - JOUR
AU  - A. V. Baev
AU  - N. V. Kutsenko
TI  - Identification of a dissipation coefficient by a variational method
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1882
EP  - 1893
VL  - 46
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a14/
LA  - ru
ID  - ZVMMF_2006_46_10_a14
ER  - 
%0 Journal Article
%A A. V. Baev
%A N. V. Kutsenko
%T Identification of a dissipation coefficient by a variational method
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1882-1893
%V 46
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a14/
%G ru
%F ZVMMF_2006_46_10_a14
A. V. Baev; N. V. Kutsenko. Identification of a dissipation coefficient by a variational method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1882-1893. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a14/

[1] Blagoveschenskii A. C., “Ob obratnoi zadache teorii rasprostraneniya seismicheskikh voln”, Probl. matem. fiz., Izd-vo Leningr. un-ta, L., 1966, 68–81

[2] Iskakov K. T., Kabanikhin S. I., “The solution of one dimensional inverse problem of geoelectrics by the method of conjugate gradients”, Rus. J. Theor. and Appl. Mech., 3 (1991), 78–88

[3] Ladyzhenskaya O. A., Smeshannaya zadacha dlya giperbolicheskogo uravneniya, Gostekhteorizdat, M., 1953

[4] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[5] Gording L., Zadacha Koshi dlya giperbolicheskikh uravnenii, Izd-vo inostr. lit., M., 1961

[6] Baev A. V., “On local solvability of inverse dissipative scattering problems”, J. Inverse and Ill-Posed Problems, 7:3 (1999), 201–220 | DOI | MR | Zbl

[7] Gaevskii X., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[8] Tikhonov A. N., “O reshenii nelineinykh integralnykh uravnenii pervogo roda”, Dokl. AN SSSR, 156:6 (1964), 1296–1299 | Zbl

[9] Denisov A. M., Vvedenie v teoriyu obratnykh zadach, Izd-vo MGU, M., 1994

[10] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR