On the peculiarities of solving the coefficient inverse problem of heat conduction for a two-part layer

A. O. Vatulyan ; S. A. Nesterov

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 4, pp. 409-423

Résumé

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.

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