On the new nonlinear properties of the nonlinear heat conductivity problem in nondivergence form

In this article, we discuss one problem of nonlinear thermal conductivity with double nonlinearity; an exact analytical solution has been found for it, the analysis of which allows revealing a number of characteristic features of thermal processes in nonlinear media. The following nonlinear effects have been established: the inertial effect,the finite propagation velocity of thermal disturbances, the spatial localization of heat, and the effect of the finite time of the existence of a thermal structure in an absorption medium.