Proceedings of the International scientific and practical conference ―Current Issues in Science‖ (January 9-11, 2026) / Publisher website: www.naukainfo.com. – Dresden, Germany, 2026. – 179 p.

148 PHYSICAL AND MATHEMATICAL SCIENCES UDC 531.1 Barabash Galyna Ph. D. (Phys.-Math.), Assoc. Prof. Ivan Franko National University of Lviv Lviv, Ukraine Onyshkevych Volodymyr Ph. D. (Phys.-Math.), Assoc. Prof. Ukrainian National Forestry University Lviv, Ukraine MATHEMATICAL MODEL OF THE UNSTEADY CONTACT TRIBOLOGICAL PROBLEM Abstract. Friction heating of system punch – elastic half plane when sliding along creative line, is considered. Using of modified conditions of heat contact in mathematical model of contact thermoelasticity, taking into account of heat generation, is proposed. In order to obtain the unknown contact area, the iterative scheme based on a control of a sign of normal stresses in the immediate contact interaction zones is used. Method of moving line of separation of boundary conditions is proposed. Key words: tribology, contact, friction, heating, thermal conductance. Introductions. The variety of factors affecting the thermal conditions of a frictional couple results in complexity of the simulation of this problem. Among these