Оптимальное управление в математических моделях соболевского типа высокого порядка с (A,p)-ограниченными операторами

O. N. Tsyplenkova

Authors

O. N. Tsyplenkova South Ural State University

Keywords:

Sobolev-type equations, strong solutions, optimal control

Abstract

This article deals with the optimal control problem for an incomplete Sobolev-type equation of high order. We prove an existence and uniqueness theorem for strong solutions to the initial value problem for a given equation. We obtain sufficient and necessary conditions for the existence and uniqueness of optimal control of these solutions. We use the ideas and methods developed by G.A. Sviridyuk and his school. The proof of the existence and uniqueness of optimal control rests on the theory of optimal control developed by J.-L. Lions.

Author Biography

O. N. Tsyplenkova, South Ural State University

Department of mathematical physics equations

References

. Demidenko G.V. Uspenskii S.V. Partial Differential Equations and Systems not Solvable with Respect to the Highest-Order Derivative. N.Y.; Basel; Hong Kong, Marcel Dekker, Inc., 2003.

Al'shin A. B, Korpusov M.O., Sveshnikov A.G. Blow-up in Nonlinear Sobolev-type Equations. Berlin; N.-Y., Walter de Gruyter, 2011. DOI: 10.1515/9783110255294

Sviridyuk G.A. Fedorov V.E. Linear Sobolev Type Equations and Degenerate SemiGroups of Operators. Utrecht; Boston; Koln; Tokyo, VSP, 2003. DOI: 10.1515/9783110915501

Keller A.V. [Numerical Solution of the Start Control for a System of Equation of Leontief Type]. Obozrenie prikladnoy i promyshlennoy matematiki, 2009, vol. 16, issue 2, pp. 345-346.

Manakova N.A. Optimal Control Problem for the Oskolkov Nonlinear Filtration Equation. Differential Equations, 2007, vol. 43, no. 9, pp. 1213-1221. DOI: 10.1134/S0012266107090042

Zamyshlyaeva, A.A. Lineynye uravneniya sobolevskogo tipa vysokogo poryadka [Linear Sobolev Type Equations of High Order]. Chelyabinsk, Publ. Center of the South Ural State University, 2012.

Zamyshlyaeva, A.A. Bychkov, E.V. [On Numerical Investigation of Mathematical Model of Waves in Shallow Water]. Matematicheskie zametki YaGU, 2013, vol. 20, no. 1, pp. 27-34.

Lions J.-L. Controle optimal de syst'emes gouvernes par des equations aux derivees partielles. Dunod, Paris, 1968.