MATHEMATICAL MODELS AND METHODS OF SOLVING SPATIAL GENERALIZED BOUNDARY VALUE PROBLEM HEAT ROTATING HOLLOW PIECEWISE HOMOGENEOUS CYLINDER

The article deals with the issues of mathematical modeling of technological systems that contain physical fields’ sources. It is believed that in the case of a simple spatial form of the object under study, the boundary value problems will be correct. The interest lies in mathematical models for nonlinear, multilayer objects under the influence of load sources, for which, using the traditional theory of existence and unity, it is impossible to guarantee the correctness of boundary value problems. The author considers boundary value problems for systems of differential and pseudo differential equations in a multilayer medium which describe the state of the studied systems under the action of discrete load sources. The correctness of such problems is proven using the theory of distributions over the space of generalized functions. The object of research is boundary value problems for systems of differential and pseudo differential equations in a multilayer medium. The aim of the research is to build correct boundary value problems, which underlie the calculated mathematical models of the process of action of physical fields on multilayer objects. The necessary and sufficient conditions for the correctness of the parabolic boundary value problem in the space of generalized functions are obtained in the article. It is shown that its solution is infinitely differentiated by a spatial variable. The results of the research can be used to obtain the conditions for the correctness of the boundary value problem for differential equations with variable coefficients. Note that, in some cases, the correctness of the calculated mathematical models determines the correctness of applied optimization mathematical models. The application of the author's research is possible when proving the correctness of boundary value problems for a number of technological processes. The universality of the research allows to widely usage of the results obtained in this work to improve the quality of technological processes.

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The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks

Environment Technology Resources Proceedings of the International Scientific and Practical Conference ◽

10.17770/etr2013vol1.833 ◽

2015 ◽

Vol 1 ◽

pp. 87

Author(s):

Ērika Teirumnieka ◽

Ilmārs Kangro ◽

Edmunds Teirumnieks ◽

Harijs Kalis

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Mass Transfer ◽

Finite Difference ◽

Boundary Value Problem ◽

Mathematical Models ◽

Boundary Value ◽

Finite Difference Methods ◽

Difference Methods ◽

The Mathematical Model

The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

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Nonlinear differential game “pursuit-evasion”: information aspect.

Informatization and communication ◽

10.34219/2078-8320-2021-12-5-111-116 ◽

2021 ◽

Vol 5 ◽

Author(s):

◽

Keyword(s):

Boundary Value Problem ◽

Mathematical Models ◽

Differential Game ◽

Boundary Value ◽

Quality Criterion ◽

Practical Consideration ◽

Pursuit Evasion ◽

Nonlinear Differential Game

The article deals with the information aspects of the nonlinear differential game “pursuit-evasion”. The mini- max quality criterion (the price of the game), mathematical models of the movement of the same type of players are set. The main problem that arises in the practical consideration of a nonlinear differential game is the solution of a boundary value problem. It is proved that: 1) a differential game can be represented as an envelope of a family of singular curves (“instantaneous solutions”) constructed from each of its points, 2) the control of the players can be found on this family. The method of constructing instant solutions is justified. The principle of information dualism in the differential game “pursuit-evasion” is proved. Its use facilitates the solution of information and computational problems that arise during the implementation of the game.

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