Engineering Physics Annotation << Back About one Method for Solving a Hyperbolic Equation Movement of Thermal Shock Waves Pashin A.V., Kudinov I.V., Mikheeva G.V. In relation to the hyperbolic heat equation, using the integral Laplace transform, an exact analytical solution to the boundary value problem of the propagation of thermal shock waves in a plate with a thermal shock on its outer surface is obtained. A detailed analysis of the obtained solution showed that, depending on the dimensionless thickness of the plate, it describes two variants of temperature changes: a) heat exchange with a temperature jump at the front (separating the heated and unheated parts of the plate), observed for large dimensionless thicknesses (l0 > π), while the temperature jump fades , not reaching the center of the plate with a subsequent diffusion change in temperature, coinciding with the classical exact analytical solution of the parabolic heat equation; b) a wave change in temperature observed for small thicknesses of the plate (l0 < π), with an oscillation frequency depending on the thickness of the plate and with an amplitude that decays exponentially until a stationary state is reached. The oscillation frequency increases with decreasing plate thickness. The oscillation process in this case occurs in the virtual absence of a temperature gradient along the spatial variable. The classical concept of temperature in this case loses its meaning. In this connection, in this work, the square of the amplitude of the wave function is taken as the temperature. Keywords: hyperbolic heat equation, integral Laplace transform, exact analytical solution, fi nite speed of heat propagation, thermal shock waves, squared wave function amplitude. DOI: 10.25791/infi zik.4.2024.1398 Pp. 27-36.