scholarly journals HYPERBOLIC MODEL OF NON -STATIONARY THERMAL CONDUCTIVITY

2016 ◽  
Vol 11 (2) ◽  
pp. 74-80 ◽  
Author(s):  
E. M. Kartashov ◽  
I. V. Antonova
Keyword(s):  
Thermal Conductivity ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Operational Calculus ◽  
Hyperbolic Model ◽  
Complex Class ◽  
Transport Models ◽  
Exact Analytical Solutions ◽  
Correct Formulation

The article presents fundamentally new results on the analytical theory of thermal conductivity for hyperbolic transport models. The questions of the correct formulation of boundary value problems are considered. A technique for finding exact analytical solutions of a rather complex class of boundary value problems based on the method of Green's functions and operational calculus is developed.

scholarly journals A Successive Linearization Method Approach to Solve Lane-Emden Type of Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Linearization Method ◽  
Exact Analytical Solutions ◽  
Successive Linearization Method ◽  
Method Approach ◽  
Better Than

We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and performs better than some numerical methods.

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

scholarly journals Completeness of the system of eigenfunctions of the Sturm-Liouville problem with the singularity

2020 ◽  
Vol 30 (1) ◽  
pp. 59-63
Author(s):  
V.P. Tanana
Keyword(s):  
Thermal Conductivity ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Liouville Problem ◽  
Discontinuous Coefficients ◽  
Order Differential Operator ◽  
Temperature Conductivity ◽  
Inverse Boundary ◽  
Sturm Liouville ◽  
Inverse Boundary Value Problems

Mathematical modeling of composite materials plays an important role in modern technology, and the solution and study of inverse boundary value problems of heat transfer is impossible without the use of systems of eigenfunctions of the Sturm-Liouville problem for the differential equation with discontinuous coefficients. One of the most important properties of such systems is their completeness in the corresponding spaces. This property of systems allows to prove theorems of existence and uniqueness of both direct problems and inverse boundary value problems of thermal conductivity, and also to prove numerical methods of solving such problems. In this paper, we prove the completeness of the Sturm-Liouville problem in the space $L_2[r_0,r_2]$ for a second-order differential operator with a discontinuous coefficient. This problem arises when investigating and solving the inverse boundary problem of thermal conductivity for a hollow ball consisting of two balls with different temperature conductivity coefficients. Self-conjugacy, injectivity, and positive definiteness of this operator are proved.

Steady Motion of a Thread Over a Rotating Roller

1994 ◽  
Vol 61 (1) ◽  
pp. 16-22 ◽  
Author(s):  
R.-J. Yang
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Steady Motion ◽  
Dynamic Equations ◽  
Initial Value ◽  
Perturbation Result ◽  
The Third

Dynamic equations of steady motion governing the behavior of threads over rotating arbitrary-axisymmetric rollers are derived. Various types of boundary conditions resulting in initial value or boundary value problems are discussed. Analytical solutions for the case of a circular cylinder are found. Two of the integrals obtained are exact. The third one, being a perturbation result, is thus approximate. Comparisons of results for a circular cylinder with those for tapered and parabolic rollers are made.

The Thermoelectromechanical J-Integral and the Thermal Permeability of Cracks

2008 ◽  
Vol 385-387 ◽  
pp. 569-572 ◽  
Author(s):  
Andreas Ricoeur ◽  
Meinhard Kuna
Keyword(s):  
Thermal Conductivity ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Crack Tip ◽  
J Integral ◽  
Pyroelectric Effect ◽  
Piezoelectric Coupling ◽  
Elastic Dielectric

The J-integral for cracks in structures storing elastic, dielectric and thermal energies is derived from thermodynamical fundamentals. The FEM is applied to solve thermoelectrome- chanical boundary value problems, accounting for piezoelectric coupling, thermoelasticity and the pyroelectric effect. Examples demonstrate the influence of the thermal conductivity of cracks on the loading of the crack tip.

Sign in / Sign up

Export Citation Format

Share Document