scholarly journals Mathematical modeling in task of optimal managing by savings in the middle class

2020 ◽  
Vol 224 ◽  
pp. 03002
Author(s):  
P.O. Derevyankina
Keyword(s):  
Optimal Control ◽  
Middle Class ◽  
Government Regulation ◽  
Real Data ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Simulation Software ◽  
Lagrange Principle ◽  
Initial Boundary Value ◽  
Active Cluster

Consumption and saving balance issues in the middle class, as the most economically active cluster of society, are the subject of extensive expert discussion and require systematic government regulation. The present paper deals with mathematical model of middle class differentiation by savings which dynamics is described by initial boundary value problem with a parabolic equation. This study aims to investigate a case of savings regulation by changing of non-savers share. The paper presents formulation this problem as an optimal boundary control problem for distributed system of savings. Based on the Lagrange principle, the necessary conditions for the solvability of the problem are derived in the form of an optimization system. The optimal control law establishing the relationship between the non-savers share and the structure of the middle class in terms of savings is obtained. The paper also considers an approach to the numerical implementation of the optimal control model in the Comsol Multiphysics simulation software. An example of model calculating for a region of Russia based on real data is given.

scholarly journals Regularized optimal control problem for a beam vibrating against an elastic foundation

2015 ◽  
Vol 63 (1) ◽  
pp. 53-71
Author(s):  
Igor Bock ◽  
Mária Kečkemétyová
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elastic Foundation ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value

Abstract We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a clamped beam against a u elastic foundation. A variable thickness of a beam plays the role of a control variable. The original equation for the deflection is regularized in order to derive necessary optimality conditions

Optimal control problem for the equation of vibrations of an elastic plate

2018 ◽  
Vol 25 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Hamlet F. Guliyev ◽  
Khayala I. Seyfullaeva
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elastic Plate ◽  
Control Function ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Necessary Condition ◽  
Necessary Condition Of Optimality ◽  
Initial Boundary Value

AbstractAn optimal control problem for the vibration equation of an elastic plate is considered when the control function is included in the coefficient of the highest order derivative and the right-hand side of the equation. The solvability of the initial boundary value problem is shown, the theorem on the existence of an optimal control is proved and a necessary condition of optimality in the form of an integral equation is obtained.

BILINEAR OPTIMAL CONTROL FOR A WAVE EQUATION

1999 ◽  
Vol 09 (01) ◽  
pp. 45-68 ◽  
Author(s):  
MIN LIANG
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Optimality System ◽  
Cost Functional ◽  
Quadratic Cost ◽  
Uniqueness Of The Solution ◽  
Initial Boundary Value ◽  
The Cost

We consider the problem of optimal control of a wave equation. A bilinear control is used to bring the state solutions close to a desired profile under a quadratic cost of control. We establish the existence of solutions of the underlying initial boundary-value problem and of an optimal control that minimizes the cost functional. We derive an optimality system by formally differentiating the cost functional with respect to the control and evaluating the result at an optimal control. We establish existence and uniqueness of the solution of the optimality system and thus determine the unique optimal control in terms of the solution of the optimality system.

scholarly journals Multi-Term Fractional Degenerate Evolution Equations and Optimal Control Problems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 483
Author(s):  
Marina Plekhanova ◽  
Guzel Baybulatova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Evolution Equations ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Fractional Equations ◽  
Initial Boundary Value ◽  
Degenerate Evolution Equations

A theorem on unique solvability in the sense of the strong solutions is proved for a class of degenerate multi-term fractional equations in Banach spaces. It applies to the deriving of the conditions on unique solution existence for an optimal control problem to the corresponding equation. Obtained results are used to an optimal control problem study for a model system which is described by an initial-boundary value problem for a partial differential equation.

scholarly journals Оптимальное управление внутривенной лазерной абляцией

2020 ◽  
Vol 128 (9) ◽  
pp. 1396
Author(s):  
А.Е. Ковтанюк ◽  
А.Ю. Чеботарев ◽  
А.А. Астраханцева ◽  
А.А. Сущенко
Keyword(s):  
Heat Transfer ◽  
Optimal Control ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Thermal Processes ◽  
Conductive Heat ◽  
Endovenous Laser Ablation ◽  
Initial Boundary Value

On the base of an initial-boundary value problem for the model of radiation-conductive heat transfer, the thermal processes that occur during endovenous laser ablation are studied. An optimal control problem is posed, which consists in approximating the solution of the initial-boundary value problem to a given temperature profile at a certain point of the model domain. The source powers going on radiation and heating the carbonized tip of the optical fiber are taken as control. An iterative algorithm for solving the problem is proposed and numerically implemented.

scholarly journals An Optimal Control Problem for A Viscoelastic Plate in a Dynamic Contact with an Obstacle

2018 ◽  
Vol 71 (1) ◽  
pp. 27-37
Author(s):  
Igor Bock ◽  
Mária Kečkemétyová
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Variable ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dynamic Contact ◽  
Viscoelastic Plate ◽  
Initial Boundary Value ◽  
Thickness Function

Abstract We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a simply supported anisotropic viscoelastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. We verify the existence of an optimal thickness function.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

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