Multipoint boundary value problem of optimal control for parabolic equations with degeneration

Pukal's'kyi, I. D.; Yashan, B. O.

doi:10.15407/mmpmf2020.63.4.17-33

Mat. Met. Fiz. Mekh. Polya

2020

DOI: 10.15407/mmpmf2020.63.4.17-33

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Multipoint boundary value problem of optimal control for parabolic equations with degeneration

I. D. Pukal's'kyi,

B. O. Yashan

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2023

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Cited by 2 publications

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“…The popularity of this kind of research is connected with its active use in solving problems of natural science, in particular hydro and gas dynamics, heat physics, diffusion, and theory of biological populations.The basics of the theory of optimal control of deterministic systems described by equations with partial derivatives were systematically described for the first time in the monograph [1]. A papers [2][3][4][5] are devoted to the problems of choosing the optimal control of systems described by parabolic boundary value problems with limited internal, starting and boundary control. Problems for high-order degenerate elliptic equations in a half-space are studied in the paper [10].…”

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Optimal control in the boundary value problem for elliptic equations with degeneration

Pukal’skii

Yashan

2023

Mat. Stud.

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The problem of optimal control of the system described by the oblique derivative problem forthe elliptic equation of the second order is studied. Cases of internal and boundary managementare considered. The quality criterion is given by the sum of volume and surface integrals.The coefficients of the equation and the boundary condition allow power singularities of arbitraryorder in any variables at some set of points. Solutions of auxiliary problems with smooth coefficients are studied to solve the given problem. Using a priori estimates, inequalities are established for solving problems and their derivatives in special H\"{o}lder spaces. Using the theorems of Archel and Riess, a convergent sequence is distinguished from a compact sequence of solutions to auxiliary problems, the limiting value of which will bethe solution to the given problem. The necessary and sufficient conditions for the existence of the optimal solution of the systemdescribed by the boundary value problem for the elliptic equation with degeneracy have been established.

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Optimal control in the boundary value problem for elliptic equations with degeneration

Pukal’skii

Yashan

2023

Mat. Stud.

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Optimal Control in the Dirichlet Problem for Elliptic Equations With Degeneration

Pukalskyy,

Yashan

2023

BMJ

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The theory of optimal control of systems, which is described by partial differential equations, is rich in results and is actively developing nowadays. The popularity of this kind of research is connected with its active use in solving problems of natural science, in particular hydro and gas dynamics, heat physics, diffusion, and the theory of biological populations. The problem of optimal control of the system described by the Dirichlet problem for the elliptic equation of the second order is studied. Cases of internal control are considered. The quality criterion is given by the volumetric integral. The coefficients of the equation admit power singularities of arbitrary order in any variables at some set of points. Solutions of auxiliary problems with smooth coefficients are studied to solve the given problem. Using a priori estimates, inequalities are established for solving problems and their derivatives in special Hölder spaces. Using the theorems of Archel and Riess, a convergent sequence is distinguished from a compact sequence of solutions to auxiliary problems, the limiting value of which will be the solution to the given problem. The necessary and sufficient conditions for the existence of the optimal solution of the system described by the Dirichlet problem for the elliptic equation with degeneracy have been established.

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Multipoint boundary value problem of optimal control for parabolic equations with degeneration

Cited by 2 publications

References 8 publications

Optimal control in the boundary value problem for elliptic equations with degeneration

Optimal control in the boundary value problem for elliptic equations with degeneration

Optimal Control in the Dirichlet Problem for Elliptic Equations With Degeneration

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