A one-dimensional model of friction contact of two different plane parallel layers has been considered. The lower surface of the first layer is rigidly fixed and the second layer is moving with constant speed over the first one and pressed to it. As a result of friction by Amonton's law on the contact surface the heat is formed. Considering that the thermal loading on the fixed surface is unknown the inverse problem on determining temperature field was formulated in terms of the temperature and displacements on the upper surface of the second layer. The correctness of the problem was investigated, using the analysis of roots of characteristic equation. The numerical comparative analysis of this problem and a direct one proved the reliability of the obtained results.
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