OPTIMAL CONTROL OF SOLUTIONS TO CAUCHY PROBLEM FOR SOBOLEV TYPE EQUATION OF HIGHER ORDER

O. N. Tsyplenkova

Abstract


An optimal control problem for the higher order Sobolev type equation  with a relatively polynomially bounded operator pencil is considered. The existence and uniqueness of a strong solution to the Cauchy problem for this equation are proved. Sufficient conditions for the existence and uniqueness of an optimal control of such solutions are obtained.

Keywords


Sobolev-type equations, relatively polynomially bounded operator pencil, strong solutions, optimal control.

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References


Sviridyuk G.A., Efremov A.A. Optimal Control of Sobolev-Type Linear Equations with Relatively p-sectorial Operators. Differential Equations, 1995, vol. 31, no. 11, pp. 1882-1890.

Sviridyuk G.A., Fedorov V.E. Linear Sobolev Type Equations and Degenerate Semigroups of Operators. Utrecht, Boston, Koln, Tokyo, VSP, 2003.

Manakova N.A., Dyl'kov A.G. Optimal Control of the Solutions of the Initial-Finish Problem for the Linear Hoff Model. Mathematical Notes, 2013, vol. 94, issue 1-2, pp. 220-230. DOI:10.1134/S0001434613070225

Keller A.V., Sagadeeva M.A. Numerical Solution of Optimal and Hard Control for Nonstationary System of Leontiev's Type. Scientific Statement of the Belgorod State University. Series "Mathematics. Physics", 2013, vol. 32, no 32, pp. 57-66. (in Russian)

Ruzakova O.A., Oleynik E.A.On the Controllability of Linear Sobolev Type Equations with Relatively Sectorial Operator Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming & Computer Software", 2012, no. 5(264), issue 11, pp. 54-61. (in Russian)

Balachandran K., Dauer J.P. Controllability of Sobolev-Type Integro-differential Systems in Banach Spaces. Journal of Mathematical Analysis and Applications, 1998, vol. 217, issue 2, pp. 335-348.

Zamyshlyaeva A. The Higher-Order Sobolev-Type Models Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming & Computer Software", 2014, vol. 2, no. 2, pp. 5-28. DOI:10.14529/mmp140201. (in Russian)

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


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