THE NUMERICAL SOLUTION TO THE OPTIMAL CONTROL PROBLEM FOR THE NONSTATIONARY DZEKTSER MODEL
Main Article Content
Abstract
Of concern is a numerical solution to the optimal control problem for the operator differential equation, unsolved with respect to the derivative by time, with Showalter Sidorov condition. Such equations are called Sobolev type equations. Sobolev type equations now constitute a vast area of nonclassical equations of mathematical physics. So in this article we construct a numerical solution to the optimal control problem for the nonstationary Dzektser model with Showalter - Sidorov condition. Besides the introduction and bibliography article comprises three parts. The first part provides essential information regarding the theory of relatively p-sectorial operators. Also in this part the existence of solutions for optimal control problem with Showalter-Sidorov condition. The optimal control problem over solutions of Dzektser model is described in the second part. The third one contains the results of the numerical solution of optimal control problem for Dzektser model considered on a rectangle.
Article Details
References
Sviridyuk G.A., Fedorov V.E. Linear Sobolev Type Equations and Degenerate Semigroups of Operators. Utrecht, Boston, K"oln, Tokyo, VSP, 2003.
Dzektser E.S. Generalization of the motion of the fluid with free surface. Dokl. Acad. Nauk SSSR, 1972, vol.202, no.5. pp.1031 - 1033. (in Russian)
Demidenko G.V., Uspenskii S.V. Equations and Systems that are not allowed for the highest derivative. Novosibirsk, Nauka Publ., 1998. (in Russian)
Sviridyuk G.A., Zagrebina S.A. Nonclassical Mathematical Physics Models. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming & Computer Software", 2012, no.40(229), pp. 7-18. (in Russian)
Sviridyuk G.A., Zagrebina S.A. The Showalter - Sidorov Problem as Phenomena of the Sobolev-Type Equations. The Bulletin of Irkutsk State University. Series "Mathematics", 2010, vol.3, no.1, pp.51-72. (in Russian)
Shestakov A.L., Keller A.V., Nazarova E.I. Numerical Solution of the Optimal Measurement Problem. Automation and Remote Control, 2012, vol.73, no.1, pp.97-104. DOI: 10.1134/S0005117912010079
Manakova N.A. Optimal Control Problem for Semilinear Sobolev Type Equations. Chelyabinsk, Publ. Center of the SUSU, 2012. (in Russian)
Sviridyuk G.A., Manakova N.A. An Optimal Control Problem for the Hoff Equation. Journal of Applied and Industrial Mathematics, 2007, vol.1, no.2, pp.247-253. DOI:10.1134/S1990478907020147
Zamyshlyaeva A.A., Tsyplenkova O.N. Optimal Control of Solutions of the Showalter - Sidorov - Dirichlet Problem for the Boussinesq - Love Equation. Differential Equations, 2013, vol.49, no.11, pp.1356-1365. DOI: 10.1134/S0012266113110049
Sagadeeva M.A., Badoyan A.D. The Problem of Optimal Control over Solutions of the Nonstationary Barenblatt - Zheltov - Kochina Model. Bulletin of the South Ural State University. Series "Computer technologies, automatic control & radioelectronics", 2014, vol.14, no.2, pp.5-11. (in Russian)
Sagadeeva M.A., Badoyan A.D. The Optimal Control over Solutions of Special Form of Nonstacionary Sobolev Type Equations in Relatively Spectral Case. Vestnik Magnitogorskogo gosudarstvennogo universiteta. Matematika The Bulletin of Magnitogorsk State Universuty. Mathematics, 2013, issue15, pp.68-80. (in Russian)
Keller A.V., Sagadeeva M.A. The Numerical Solution of Optimal and Hard Control for Nonstationary System of Leontiev Type. Nauchnye vedomosti BelGU. Seriya "Matematika i fizika". Belgorod State University Scientific Bulletin. Series "Mathematics and Physics", 2013, vol.32, no.19, pp.57-66. (in Russian)