Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Vatulyan A. O., Nesterov S. A. On the Peculiarities of Solving the Coefficient Inverse Problem of Heat Conduction for a Two-Part Layer. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2019, vol. 19, iss. 4, pp. 409-423. DOI: 10.18500/1816-9791-2019-19-4-409-423, EDN: FWBUCB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
02.12.2019
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
536.24
DOI: 
10.18500/1816-9791-2019-19-4-409-423
EDN: 
FWBUCB

On the Peculiarities of Solving the Coefficient Inverse Problem of Heat Conduction for a Two-Part Layer

Autors: 
Vatulyan Alexander Ovanesovitsch, Southern Federal University
Nesterov Sergey A., Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences
Abstract: 

The coefficient inverse problem of thermal conductivity about the determination of the thermophysical characteristics of the functional-gradient part of a two-component layer is posed. The input information is the temperature measurement data on the top face of the layer. After the Laplace transform and dimensioning, the direct problem of heat conduction is solved on the basis of Galerkin projection method. Conversion of transformant on the basis of the theory of residues is carried out. The influence of various laws of changes in the thermophysical characteristics and thickness of the functional-gradient part on the input information was studied. To solve the inverse problem, two approaches are used. The first approach is based on the algebraization of the direct problem using Galerkin projection method. The second approach is a development of the previously developed iterative approach, at each step of which the Fredholm integral equation of the first kind is solved. Computational experiments were carried out to restore various laws of change in thermophysical characteristics. Practical advice on the choice of a time interval for additional information is given. A comparison of two approaches to solving the coefficient inverse problem of heat conduction is made. 

Key words: 
thermal conductivity coefficient
specific heat capacity
layered materials
functional-gradient materials
inverse problem
identification
algebraization
iterative scheme
integral equation
Galerkin projection method
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Received: 
23.05.2019
Accepted: 
30.06.2019
Published: 
02.12.2019
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