Geodesic
Optimal control of solutions to the initial-final problem for the Sobolev type equation of higher order
Journal of computational and engineering mathematics, Tome 3 (2016) no. 2, pp. 57-67.

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Of concern is the optimal control problem for the Sobolev type higher order equation with relatively polynomially bounded operator pencil. The theorem of existence and uniqueness of strong solutions to the initial-final problem for abstract equation is proved. The sufficient conditions for optimal control existence and uniqueness of such solutions are found. We use the ideas and methods developed by G.A. Sviridyuk and his disciples.
Keywords: Sobolev type equations, relatively polynomially bounded operator pencil, strong solutions, optimal control. 
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A. A. Zamyshlyaeva; O. N. Tsyplenkova; E. V. Bychkov. Optimal control of solutions to the initial-final problem for the Sobolev type equation of higher order. Journal of computational and engineering mathematics, Tome 3 (2016) no. 2, pp. 57-67. http://geodesic.mathdoc.fr/item/JCEM_2016_3_2_a6/

[1] S. A. Zagrebina, “Nachalno-konechnaya zadacha dlya lineinoi sistemy Nave–Stoksa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 7, 35–39 | Zbl

[2] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, Inverse and Ill-Posed Problems Series, 42, de Gruyer, 2012, 216+viii pp. | DOI | MR

[3] A. V. Keller, “Chislennoe reshenie zadachi startovogo upravleniya dlya sistemy uravnenii leontevskogo tipa”, Obozrenie prikladnoi i promyshlennoi matematiki, 16:2 (2009), 345–346

[4] A. V. Keller, “Algoritm resheniya zadachi Shouoltera–Sidorova dlya modelei leontevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 7, 40–46 | Zbl

[5] A. V. Keller, E. I. Nazarova, “Zadacha optimalnogo izmereniya: chislennoe reshenie, algoritm programmy”, Izv. Irkutskogo gos. un-ta. Ser. Matematika, 4:3 (2011), 74–82 | Zbl

[6] G. A. Sviridyuk, A. A. Efremov, “Optimal control of Sobolev-type linear equations with relatively $p$-spectorial operators”, Differential Equations, 31:11 (1996), 1882–1890 | MR | Zbl

[7] N. A. Manakova, “Optimal control problem for the Oskolkov nonlinear filtration equation”, Differential Equations, 43:9 (2007), 1213–1221 | DOI | MR | Zbl

[8] N. A. Manakova, A. G. Dylkov, “Optimalnoe upravlenie resheniyami nachalno-konechnoi zadachi dlya lineinykh uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 8, 113–114 | Zbl

[9] S. A. Zagrebina, “Nachalno-konechnye zadachi dlya neklassicheskikh modelei matematicheskoi fiziki”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:2 (2013), 5–24 | Zbl

[10] S. A. Zagrebina, M. A. Sagadeeva, “Obobschennaya zadacha Shouoltera – Sidorova dlya uravnenii sobolevskogo tipa s silno $(L,p)$-radialnym operatorom”, Vestnik MaGU. Matematika, 2006, no. 9, 17–27, MaGU, Magnitogorsk | Zbl

[11] G. A. Sviridyuk, N. A. Manakova, “Dinamicheskie modeli sobolevskogo tipa s usloviem Shouoltera–Sidorova i additivnymi «shumami»”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:1 (2014), 90–103 | DOI | Zbl

[12] A. Favini, G. A. Sviridyuk, A. A. Zamyshlyaeva, “One Class of Sobolev Type Equations of Higher Order with Additive “White Noise””, Communications on Pure and Applied Analysis, 15:1 (2016), 185–196 | DOI | MR | Zbl

[13] A. Favini, G. A. Sviridyuk, N. A. Manakova, “Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises””, Abstract and Applied Analysis, 2015 (2015), 697410, 8 pp. | DOI | MR | Zbl

[14] A. V. Keller, A. L. Shestakov, G. A. Sviridyuk, Yu. V. Khudyakov, “The Numerical Algorithms for the Measurement of the Deterministic and Stochastic Signals”, Semigroups of Operators – Theory and Applications, Proc. Int. Conference (Bedlewo, Poland, 2013, October 6–10), Springer Proceedings in Mathematics and Statistics, 113, eds. J. Banasiak, A. Bobrowski, M. Lachowicz, Springer International Publishing, 2015, 183–195 | DOI | MR | Zbl

[15] N. A. Manakova, G. A. Sviridyuk, “An Optimal Control of the Solutions of the Initial-Final Problem for Linear Sobolev Type Equations with Strongly Relatively p-Radial Operator”, Semigroups of Operators – Theory and Applications, Proc. Int. Conference (Bedlewo, Poland, 2013, October 6–10), Springer Proceedings in Mathematics and Statistics, 113, eds. J. Banasiak, A. Bobrowski, M. Lachowicz, Springer International Publishing, 2015, 213–224 | DOI | MR | Zbl

[16] M. A. Sagadeeva, G. A. Sviridyuk, “The Nonautonomous Linear Oskolkov Model on a Geometrical Graph: the Stability of Solutions and Optimal Control Problem”, Semigroups of Operators – Theory and Applications, Proc. Int. Conference (Bedlewo, Poland, 2013, October 6–10), Springer Proceedings in Mathematics and Statistics, 113, eds. J. Banasiak, A. Bobrowski, M. Lachowicz, Springer International Publishing, 2015, 257–271 | DOI | MR | Zbl

[17] A. L. Shestakov, G. A. Sviridyuk, Yu. V. Khudyakov, “Dynamical Measurements in the View of the Group Operators Theory”, Semigroups of Operators – Theory and Applications, Proc. Int. Conference (Bedlewo, Poland, 2013, October 6–10), Springer Proceedings in Mathematics and Statistics, 113, eds. J. Banasiak, A. Bobrowski, M. Lachowicz, Springer International Publishing, 2015, 273–286 | DOI | MR | Zbl

[18] S. A. Zagrebina, E. A. Soldatova, G. A. Sviridyuk, “The Stochastic Linear Oskolkov Model of the Oil Transportation by the Pipeline”, Semigroups of Operators – Theory and Applications, Proc. Int. Conference (Bedlewo, Poland, 2013, October 6–10), Springer Proceedings in Mathematics and Statistics, 113, eds. J. Banasiak, A. Bobrowski, M. Lachowicz, Springer International Publishing, 2015, 317–326 | DOI | MR

[19] A. A. Zamyshlyaeva, G. A. Sviridyuk, “The Linearized Benney – Luke Mathematical Model with Additive White Noise”, Semigroups of Operators – Theory and Applications, Proc. Int. Conference (Bedlewo, Poland, 2013, October 6–10), Springer Proceedings in Mathematics and Statistics, 113, eds. J. Banasiak, A. Bobrowski, M. Lachowicz, Springer International Publishing, 2015, 327–336 | DOI | MR

[20] A. A. Zamyshlyaeva, “Fazovye prostranstva odnogo klassa lineinykh uravnenii sobolevskogo tipa vtorogo poryadka”, Vychislitelnye tekhnologii, 8:4 (2003), 45–54 | Zbl

[21] A. A. Zamyshlyaeva, E. V. Bychkov, “Fazovoe prostranstvo modifitsirovannogo uravneniya Bussineska”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 12, 13–19 | Zbl

[22] S. A. Zagrebina, A. S. Konkina, “The multipoint initial-final value condition for the Navier–Stokes linear model”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:1 (2015), 132–136 | DOI | Zbl

[23] E. V. Bychkov, “Ob odnoi polulineinoi matematicheskoi modeli sobolevskogo tipa vysokogo poryadka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:2 (2014), 111–117 | DOI | MR | Zbl

[24] A. A. Zamyshlyaeva, E. V. Bychkov, O. N. Tsyplenkova, “Mathematical models based on Boussinesq–Love equation”, Applied Mathematical Sciences, 8:110 (2014), 5477–5483 | DOI

[25] A. A. Zamyshlyaeva, “Fazovoe prostranstvo uravneniya sobolevskogo tipa vysokogo poryadka”, Izv. Irkutskogo gos. un-ta. Ser. Matematika, 4:4 (2011), 45–57 | Zbl

[26] A. A. Zamyshlyaeva, Lineinye uravneniya sobolevskogo tipa vysokogo poryadka, Izd. tsentr YuUrGU, Chelyabinsk, 2012, 107 pp. | MR

[27] A. A. Zamyshlyaeva, “Matematicheskie modeli sobolevskogo tipa vysokogo poryadka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:2 (2014), 5–28 | DOI | Zbl

[28] O. Tsyplenkova, “Optimal control of solutions to Cauchy problem for Sobolev type equation of higher order”, J. Comp. Eng. Math., 1:2 (2014), 62–67 | MR | Zbl