scholarly journals On One Mathematical Model Described by Boundary Value Problem for the Biharmonic Equation

2016 ◽  
Vol 9 (4) ◽  
pp. 40-52 ◽  
Author(s):  
V.V. Karachik ◽  
◽  
B.T. Torebek ◽  
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Biharmonic Equation ◽  
Boundary Value

Mathematical model implementation in conditions of uncertainty and possible risks

2021 ◽  
pp. 137-145
Author(s):  
A. Kravtsov ◽  
◽  
D. Levkin ◽  
O. Makarov ◽  
◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Layer Structure ◽  
Boundary Value ◽  
Goal Function ◽  
Cauchy Problems ◽  
System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

The Initial Boundary-Value Problem for a Mathematical Model for Granular Medium

2015 ◽  
Vol 725-726 ◽  
pp. 863-868
Author(s):  
Vladimir Lalin ◽  
Elizaveta Zdanchuk
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Stress Tensor ◽  
Granular Medium ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Cosserat Continuum ◽  
Suitable Model ◽  
Initial Boundary Value

In this work we consider a mathematical model for granular medium. Here we claim that Reduced Cosserat continuum is a suitable model to describe granular materials. Reduced Cosserat Continuum is an elastic medium, where all translations and rotations are independent. Moreover a force stress tensor is asymmetric and a couple stress tensor is equal to zero. Here we establish the variational (weak) form of an initial boundary-value problem for the reduced Cosserat continuum. We calculate the variation of corresponding Hamiltonian to obtain motion differential equation.

scholarly journals Biharmonic Equation on Annulus in a Unit Sphere with Polynomial Boundary Condition

2017 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Ikhsan Maulidi ◽  
Agah D Garnadi
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Unit Sphere ◽  
Biharmonic Equation ◽  
Boundary Value ◽  
Boundary Function ◽  
Exact Algorithms ◽  
Polynomial Functions ◽  
Dirichlet Conditions ◽  
Laplace Equations

We studied Biharmonic boundary value problem on annulus with polynomial data. We utilize an exact algorithms for solving Laplace equations with Dirichlet conditions with polynomial functions data. The algorithm requires differentiation of the boundary function, but no integration.

Mathematical model of magnetic field for a sectorial ferromagnetic cylinder

2021 ◽  
Vol 2021 (49) ◽  
pp. 19-25
Author(s):  
R. M. Dzhala ◽  
◽  
V. R. Dzhala ◽  
B. I. Horon ◽  
B. Ya. Verbenets ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Spatial Distribution ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Algebraic Equations ◽  
Secondary Field

The solution of the boundary-value problem of magnetostatics for a circular ferromagnetic cylinder with a longitudinal sectorial cutout is described. The external primary magnetic field is orthogonal to the cylinder and directed at arbitrary azimuth relative to the cutout. A system of algebraic equations for finding the amplitudes of azimuthal expansions of the spatial distribution of the secondary field of the outer and sectorial partial regions of the cylinder is obtained by the method of rearrangement of functions.

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