Geodesic
Reconstruction of boundary controls in reaction--convection--diffusion model
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 85-92.

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In this paper, the problem of reconstruction of boundary controls for the stationary reaction–convection–diffusion model is considered. This problem is ill-posed. The root mean square norm and the total variation of control are used as a stabilizer in the Tikhonov functional. Results of numerical experiments are present.
Mots-clés : reaction–convection–diffusion model
Keywords: boundary controls, ill-posed problem, variational method. 
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A. I. Korotkii; Yu. V. Starodubtseva. Reconstruction of boundary controls in reaction--convection--diffusion model. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 85-92. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a10/

[1] Marchuk G. I., Mathematical modeling in environmental problem, Nauka, M., 1982, 319 pp.

[2] Samarskii A. A., Vabishchevich P. N., Computational heat transfer, Editorial URSS, M., 2003, 784 pp.

[3] Samarskii A. A., Vabishchevich P. N., Numerical methods for solving inverse problems of mathematical physics, Editorial URSS, M., 2004, 478 pp.

[4] Kabanikhin S. I., Inverse and ill-posed problem, Sibirskoe nauchnoe izdatel'stvo, Novosibirsk, 2009, 457 pp.

[5] Korotkii A. I., Kovtunov D. A., “Reconstruction of boundary regimes in the inverse problem of thermal convection of a high-viscosity fluid”, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 12, no. 2 (2006), 88–97 (in Russian)

[6] Ladyzhenskaya O. A., Boundary value problem of mathematical physics, Nauka, M., 1973, 408 pp.

[7] Ladyzhenskaya O. A., Ural'tseva N. N., Linear and quasilinear elliptic equations, Nauka, M., 1973, 576 pp.

[8] Ladyzhenskaya O. A., Mathematical problems in the dynamics of a viscous incompressible fluid, Fizmatlit, M., 1961, 203 pp.

[9] Alekseev G. V., Tereshhko D. A., Analysis and optimization in viscous fluid hydrodynamics, Dal'nauka, Vladivostok, 2008, 365 pp.

[10] Mikhailov V. P., Partial differential equations, Nauka, M., 1976, 392 pp.

[11] Adams R. A., Sobolev spaces, Academic Press, New York, 1975, 268 pp. | MR | Zbl

[12] Sobolev S. L., Some applications of functional analysis in mathematical physics, Nauka, M., 1988, 336 pp.

[13] Lions G.-L., Optimal control of systems described by partial differential equations, Mir, M., 1972, 414 pp.

[14] Fursikov A. V., Optimal control of distributed systems. Theory and applications, Nauchnaya kniga, Novosibirsk, 1999, 352 pp.

[15] Kolmogorov A. N., Fomin S. V., Elements of the functions theory and functional analysis, Nauka, M., 1972, 496 pp.