OPTIMAL CONTROL OF SOLUTIONS OF A MULTIPOINT INITIAL-FINAL PROBLEM FOR NON-AUTONOMOUS EVOLUTIONARY SOBOLEV TYPE EQUATION

被引：11

作者：

Sagadeeva, Minzilia A. ^{[1
]}

Zagrebina, Sophiya A. ^{[1
]}

Manakova, Natalia A. ^{[1
]}

机构：

[1] South Ural State Univ, Inst Nat Sci & Math, Lenin Av 76, Chelyabinsk 454080, Russia

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2019年 / 8卷 / 03期

关键词：

Relatively p-radial operator; degenerate C-0-semiflow of solving operators; relatively spectral projections; generalized splitting theorem; strong solution; partial differential equation with complex coefficients; LINEAR-EQUATIONS; MODELS;

D O I：

10.3934/eect.2019023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper presents sufficient conditions for existence of an optimal control of solutions to a non-autonomous degenerate operator-differential evolution equation. We construct families of operators that solve this equation, as well as classical and strong solutions of the multipoint initial-final problem for the equation. We show that there exists a solution of an optimal control problem for a given operator-differential equation with a multipoint initial-final condition. The paper, in addition to the introduction and the bibliography, contains five sections. The first three parts contain information about the solvability of the multipoint initial-final problem for a non-autonomous equation. The fourth section presents the main result of the article; that is, a theorem on existence of optimal control of solutions to a multipoint initial-final problem. In the fifth part, the optimal control problem for the non-autonomous modified Chen - Gurtin model with the multipoint initial-final condition is investigated on the basis of the obtained abstract results.

引用

页码：473 / 488

页数：16

共 17 条

[1] OPTIMAL CONTROL OF SOLUTIONS TO THE MULTIPOINT INITIAL - FINAL PROBLEM FOR NONSTATIONARY RELATIVELY BOUNDED EQUATIONS OF SOBOLEV TYPE
Sagadeeva, M. A.
Badoyan, A. D.
BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2014, 7 (03): : 128 - 134
[2] An Optimal Control of the Solutions of the Initial-Final Problem for Linear Sobolev Type Equations with Strongly Relatively p-Radial Operator
Manakova, Natalia A.
Sviridyuk, Georgy A.
SEMIGROUPS OF OPERATORS - THEORY AND APPLICATIONS, 2015, 113 : 213 - 224
[3] MULTIPOINT INITIAL-FINAL PROBLEM FOR ONE CLASS OF SOBOLEV TYPE MODELS OF HIGHER ORDER WITH ADDITIVE "WHITE NOISE"
Sviridyuk, G. A.
Zamyshlyaeva, A. A.
Zagrebina, S. A.
BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2018, 11 (03): : 103 - 117
[4] MULTIPOINT INITIAL-FINAL VALUE PROBLEMS FOR DYNAMICAL SOBOLEV-TYPE EQUATIONS IN THE SPACE OF NOISES
Favini, Angelo
Zagrebina, Sophiya A.
Sviridyuk, Georgy A.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
[5] OPTIMAL CONTROL OF SOLUTIONS OF INITIAL - FINISH PROBLEM FOR THE LINEAR SOBOLEV TYPE EQUATIONS
Manakova, N. A.
Dylkov, A. G.
BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2011, (08): : 113 - 114
[6] Optimal Control of Solutions to the Showalter - Sidorov Problem for the Sobolev Type Equation of Higher Order
Zamyshlyaeva, A. A.
Tsyplenkova, O. N.
Bychkov, E., V
2016 2ND INTERNATIONAL CONFERENCE ON INDUSTRIAL ENGINEERING, APPLICATIONS AND MANUFACTURING (ICIEAM), 2016,
[7] Existence of optimal pairs and solvability of non-autonomous fractional Sobolev-type integrodifferential equations
Sharma, Madhukant
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2025, 56 (01): : 1 - 12
[8] Existence of optimal pairs and solvability of non-autonomous fractional Sobolev-type integrodifferential equations
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INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023, 56 (1): : 1 - 12
[9] Initial value problem to the second order non-autonomous functional differential-iterative equation
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延边大学学报(自然科学版), 2006, (02) : 96 - 99
[10] Asymptotic expansion of solutions to the periodic problem for a non-linear Sobolev-type equation
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Naumkin, P. I.
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IZVESTIYA MATHEMATICS, 2013, 77 (02) : 313 - 324

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