Geodesic
Study of the objectives of boundary control and final observation for the mathematical model of non-linear filtration
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 4, pp. 28-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article is devoted to studying the problem of boundary control and final observation for a degenerate mathematical model of non-linear filtration, based on the Oskolkov equation, with the initial condition of Showalter-Sidorov. This model belongs to the class of semilinear models of the Sobolian type, in which the nonlinear operator is $p$-coercive and $s$-monotonic. The paper for the first time considers the problem of boundary control and final observation for the semilinear model of the Sobolian type and establishes the conditions of the existence of the control-state pair of the matter being studied.
Keywords: problem of boundary control and final observation, mathematical model of non-linear filtration
Mots-clés : Sobolean-type equations. 
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K. V. Perevozchikova; N. A. Manakova. Study of the objectives of boundary control and final observation for the mathematical model of non-linear filtration. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 4, pp. 28-33. http://geodesic.mathdoc.fr/item/VYURM_2022_14_4_a3/

[1] A.P. Oskolkov, “Nachalno-kraevye zadachi dlya uravnenii dvizheniya nelineinykh vyazkouprugikh zhidkostei”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 17, Zap. nauchn. sem. LOMI, 147, 1985, 110–119 | Zbl

[2] V.B. Amfilokhiev, Ya.I. Voitkunskii, N.P. Mazaeva, “Techeniya polimernykh rastvorov pri nalichii konvektivnykh uskorenii”, Trudy Leningradskogo korablestroitelnogo instituta, 96 (1975), 3–9

[3] G.A. Sviridyuk, V.O. Kazak, “Fazovoe prostranstvo odnoi obobschennoi modeli Oskolkova”, Sibirskii matematicheskii zhurnal, 44:5 (2003), 1124–1131 | MR | Zbl

[4] L.A. Kovaleva, A.S. Konkina, S.A. Zagrebina, “Stochastic Barenblatt-Zheltov-Kochina Model with Neumann Condition and Multipoint Initial-Final Value Condition”, Journal of Computational and Engineering Mathematics, 9:1 (2022), 24–34 | DOI | Zbl

[5] N.A. Manakova, “Matematicheskie modeli i optimalnoe upravlenie protsessami filtratsii i deformatsii”, Vestnik YuUrGU. Seriya: Matematicheskoe modelirovanie i programmirovanie, 8:3 (2015), 5–24 | Zbl

[6] Zh.-L. Lions, Upravlenie singulyarnymi raspredelennymi sistemami, Nauka, M., 1987, 367 pp.

[7] G.A. Sviridyuk, I.N. Semenova, “Razreshimost neodnorodnoi zadachi dlya obobschennogo filtratsionnogo uravneniya Bussineska”, Differentsialnye uravneniya, 24:9 (1988), 1607–1611 | MR | Zbl