This work is devoted to the hyperbolic equation of heat conduction and the relaxation equation of heat conduction derived by the author. The hyperbolic equation of heat conduction can be considered as a special case of the more general relaxation equation of heat conduction which takes into account the relaxation of heat flux (the finite speed of heat flux propagation) and the relaxation of internal heat source capacity. The work is devided into four parts. The first chapter includes an introduction to the mathematical modelling of heat conduction in solids. The second chapter is focused on the formulation and features of the parabolic, hyperbolic and relaxation models of heat conduction. In the third chapter, selected cases of the hyperbolic heat conduction are solved by analytical and numerical methods. In the fourth chapter, the author solves a number of relaxation initial and boundary value problems using analytical, semi-analytical and numerical methods.
Most of the original solutions presented in the work have been previously published in the leading international journals, such us: International Journal of Heat and Mass Transfer, International Communications in Heat and Mass Transfer, Cryogenics, Journal of Physics D: Applied Physics, Heat and Mass Transfer.