On inclusions with multivalued operators and their applications to some optimization problems

Zvyagin, V. G.; Obukhovskiĭ, Valeri; Zvyagin, A. V.

doi:10.1007/s11784-015-0219-2

Cited by 22 publications

(8 citation statements)

References 18 publications

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“…To prove this Theorem we use topological degree theory for multivalued vector fields (see, for example, [ 32 ]). By virtue of the a priori estimate ( 47 ), all solutions of the family of operator inclusions ( 46 ) lie in the ball

of radius

centered at zero.…”

Section: Optimal Feedback Control Problemmentioning

confidence: 99%

Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model

Zvyagin

2022

Polymers

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In this paper we consider the initial–boundary value problem describing the motion of weakly concentrated aqueous polymer solutions. The model involves the regularized Jaumann’s derivative in the rheological relation. Also this model is considered with non-linear viscosity. On the basis of the topological approximation approach to the study of hydrodynamics problems the existence of weak solutions is proved. Also we consider an optimal feedback control problem for this initial–boundary value problem. The existence of an optimal solution minimizing a given performance functional is proved.

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of radius

centered at zero.…”

Section: Optimal Feedback Control Problemmentioning

confidence: 99%

Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model

Zvyagin

2022

Polymers

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“…Moreover, we recall that the multimap F takes compact values in H 2 (T, C) and that it has the properties (F 1) and (F 2). Hence, we are in the position to apply the Filippov implicit function lemma in the version furnished in ( [15], Corollary 1.15). Then we can say that there exists a Bochner-measurable selectionû : J → L 2 (T, C) of the multimap F (., Q(.))…”

Section: An Applicationmentioning

confidence: 99%

“…By using the classical arguments (see, for example [15]) the controllability of (5.1) is brought back to the existence of mild solutions for a problem described by the nonautonomous semilinear second order differential inclusion with nonlocal conditions      x (t) ∈ A(t)x(t) + F (t, x(t)), t ∈ J x(0) = g(x)…”

Section: Introductionmentioning

confidence: 99%

An existence theorem for a non-autonomous second order nonlocal multivalued problem

Cardinali

Gentili²

2017

Stud. Univ. Babes-Bolyai Math.

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Abstract. In this paper we prove the existence of mild solutions for a nonlocal problem governed by an abstract semilinear non-autonomous second order differential inclusion, where the non-linear part is an upper-Caratheodory semicontinuous multimap. Our existence theorem is obtained thanks to the introduction of a fundamental Cauchy operator. Finally we apply our main result to provide the controllability of a problem involving a non-autonomous wave equation.Mathematics Subject Classification (2010): 34A60, 34G25.

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“…Такой подход позволил исследовать задачи управления ряда моделей движения неньютоновых сред (суспензий, водных растворов полимеров, различных сред с памятью [6][7][8][9][10][11][12]), которые в силу сложности этих систем ранее были недостаточно изучены с точки зрения оптимального управления.…”

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Optimal feedback control problem for Bingham media motion with periodic boundary conditions

Zvyagin¹,

Turbin²

2019

Доклады Академии наук

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We study the optimal feedback control problem for the motion of Bingham media with periodic boundary conditions in two- and three-dimensional cases. First, the considered problem is interpreted as an operator inclusion with a multivalued right-hand side. Then, the approximation-topological approach to hydrodynamic problems and the degree theory for a class of multivalued maps are used to prove the existence of solutions of this inclusion. Finally, we prove that, among the solutions of the considered problem, there exists one minimizing the given cost functional.

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On inclusions with multivalued operators and their applications to some optimization problems

Cited by 22 publications

References 18 publications

Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model

Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model

An existence theorem for a non-autonomous second order nonlocal multivalued problem

Optimal feedback control problem for Bingham media motion with periodic boundary conditions

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