Geodesic
Numerical analysis of the inverse identification problem for the lower coefficient of an elliptic equation
Dalʹnevostočnyj matematičeskij žurnal, Tome 6 (2005) no. 1, pp. 57-70 
E. A. Kalinina. Numerical analysis of the inverse identification problem for the lower coefficient of an elliptic equation. Dalʹnevostočnyj matematičeskij žurnal, Tome 6 (2005) no. 1, pp. 57-70. http://geodesic.mathdoc.fr/item/DVMG_2005_6_1_a4/
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     title = {Numerical analysis of the inverse identification problem for the lower coefficient of an elliptic equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the inverse problem of identification of a coefficient in the two-dimensional stationary equation of diffusion – reaction is considered. For the solution of this problem the numerical algorithm is developed which is based on the two-layer gradient algorithm. Theoretical aspects and the convergence of the algorithm are discussed. The results of numerical experiments are analyzed in details.

[1] G. V. Alekseev, “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teplomassoperenosa”, Dokl. RAN, 375:3 (2000), 315–319 | MR

[2] C. V. Alekseev, E. A. Adomavichus, “Theoretical analysis of inverse extremal problems of admixture diffusion in viscous fluids”, J. Inv. Ill-Posed Problems, 9:5 (2001), 435–468 | MR | Zbl

[3] G. V. Alekseev, E. A. Adomavichyus, “Issledovanie obratnykh ekstremalnykh zadach dlya nelineinykh statsionarnykh uravnenii perenosa veschestva”, Dalnevost. mat. zhurn., 3:1 (2002), 79–92

[4] G. V. Alekseev, “Obratnye ekstremalnye zadachi dlya statsionarnykh uravnenii teorii massoperenosa”, Zh. vychisl. matem. i matem. fiz., 42:3 (2002), 380–394 | MR | Zbl

[5] G. V. Alekseev, “Razreshimost obratnykh ekstremalnykh zadach dlya statsionarnykh uravnenii teplomassoperenosa”, Sib. mat. zhurn., 42:5 (2001), 971–991 | MR | Zbl

[6] A. N. Tikhonov, V. Ya. Arsenin, Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[7] A. G. Fatullayev, “Determination of unknown coefficient in nonlinear diffusion equation”, Nonlinear Analysis, 44 (2001), 337–344 | DOI | MR | Zbl

[8] A. G. Fatullayev, “Numerical procedure for the determination of an unknown coefficients in parabolic equations”, Comp. Phys. Comm., 144 (2002), 29–33 | DOI | MR | Zbl

[9] K. Ito, K. Kunisch, “Estimation of the convection coefficient in elliptic equations”, Inverse Problems, 13 (1997), 995–1013 | DOI | MR | Zbl

[10] A. Shidfar, K. Tavakoli, “An inverse heat conduction problem”, South. Asian Bull. Math., 26 (2002), 503–507 | DOI | MR

[11] M. Dehghan, “Finding a control parameter in one-dimensional parabolic equations”, Appl. Math. Comp., 135 (2003), 491–503 | DOI | MR | Zbl

[12] A. A. Samarskii, P. N. Vabischevich, Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki, Moskva, 2004, 480 pp.

[13] B. Lowe, W. Rundell, “The determination of a coefficient in an elliptic equation from average flux data”, J. Comput. Math., 70 (1996), 173–187 | DOI | MR | Zbl

[14] D. A. Tereshko, “Chislennoe reshenie zadach identifikatsii parametrov primesi dlya statsionarnykh uravnenii massoperenosa”, Vych. tekhn., 9:4, Spets. vyp. (2004), 92–98

[15] A. Capatina, R. Stavre, “Numerical analysis of a control problem in heat conducting Navier – Stokes fluid”, Int. J. Eng. Sci., 34:13 (1996), 1467–1476 | DOI | MR | Zbl

[16] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nauka, M., 1974, 480 pp. | MR | Zbl

[17] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980, 496 pp. | MR | Zbl