PROBLEM OF HARD AND OPTIMAL CONTROL OF SOLUTIONS TO THE INITIAL-FINAL PROBLEM FOR NONSTATIONARY SOBOLEV TYPE EQUATION

Ani Badoyan

Abstract


The main aim of this work is solving the problem of hard and optimal control of solution to the initial-finial problem for nonstationary Sobolev type equation. We construct a solution to the initial-final problem for the nonstationary equation and show that a unique optimal control of solutions to this problem exists.

Apart from the introduction and bibliography, the article consists of three sections. The first section provides the essentials of the theory of relatively p-bounded operators. In the second section we construct a~strong solution to the initial-final problem for nonstationary Sobolev-type equations. The third section contains our proof that there exists a unique optimal control of solutions to the initial-final problem.


Keywords


optimal control, initial-final problem, Sobolev-type equations, relatively bounded operator.

Full Text:

PDF

References


Favini A., Yagi A. Degenerate Differential Equations in Banach Spaces. N.Y., Basel, Hong Kong, Marcel Dekker Inc., 1999.

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.

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

Al'shin A.B., Korpusov M.O., Sveshnikov A.G. Blow-up in Nonlinear Sobolev Type Equations. Berlin, de Gruyter, 2011.

Zagrebina S.A. The Initial-Finite Problems for Nonclassical Models of Mathematical Physics. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming & Computer Software", 2013, vol. 6, no. 2, pp. 5--24. (in Russian)

Sagadeeva M.A., Badoyan A.D. Optimal Control of Solutions to the Multipoint Initial-Final Problem for Nonstationary

Relatively Bounded Equations of Sobolev Type. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming & Computer Software", 2014, vol. 7, no. 3, pp. 128--134. doi: 10.14529/mmp140314

Zagrebina S.A., Sagadeeva M.A. The Generalized Splitting Theorem for Linear Sobolev type Equations in Relatively Radial Case. The Bulletin of Irkutsk State University. Series "Mathematics", 2013, vol. 7, pp. 19--33.

Keller A.V., Sagadeeva M.A. Numerical Solution of Optimal and Hard Control for Nonstationary System of Leontiev's Type. Belgorod State University Scientific Bulletin. Series "Mathematics and Physics", 2013, vol. 32, no. 19, pp. 57--66. (in Russian)


Refbacks

  • There are currently no refbacks.


 Save