The problem of identification of functions of a system of one-dimensional equations of heat conduction and elastic waves has been considered. A condition for the uniqueness of a solution has been formulated. The instability of the solution to an inverse problem and of the problem of smoothing has been shown with the example of employment of the iterative-variational regularization method. A finite-difference scheme has been constructed for the equation of elastic waves in the presence of the dependence of its functions on temperature. A computational experiment has been conducted which confirms the instability of the inverse problem. Conclusions have been drawn on the direction of development of the regularization method for partial differential equations.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 95, No. 4, pp. 934–946, July–August, 2022.
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Vikulov, A.G. Uniqueness and Stability of a Solution to an Inverse Thermoelasticity Problem. 1. Formulation of the Problem. J Eng Phys Thermophy 95, 918–930 (2022). https://doi.org/10.1007/s10891-022-02546-3
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DOI: https://doi.org/10.1007/s10891-022-02546-3