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.
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Aripov, Mersaid and Sayfullayeva, Maftuha
"On the new nonlinear properties of the nonlinear heat conductivity problem in nondivergence form,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 3:
2, Article 8.