RESEARCH OF THE TWO-DIMENSIONAL THERMAL CONDUCTIVITY EQUATION WITH EXPONENTIAL AND EXPONENTIAL DEPENDENCES OF SOIL COEFFICIENTS ON TEMPERATURE

Abstract

This article examines a two-dimensional nonlinear heat conduction equation as applied to heat transfer processes in soil. The authors consider two cases of equation linearization: one with an exponential dependence of the heat capacity and thermal conductivity coefficients on temperature, and another with a power-law (exponential) dependence. In the first case, the problem is reduced to a second-order linear equation, for which analytical solutions are obtained in the form of classical separation of variables, plane waves, and more complex functional structures. In the second case, the solution is found in self-similar form and expressed in terms of degenerate Gaussian hypergeometric functions.