The upper estimation of the nonlinear equation of thermoconductivity with changing thermoconductivity coefficient depending on the law of any degree

In the case when the coefficient of thermal conductivity (diffusion) $g$ depends on the temperature (concentration) $c$, according to the law $g(c)=Ac^n$ (here $A - const, 1<n<\infty$) , an upper estimate is obtained for the solution of the corresponding nonlinear parabolic equation describing the process of heat (substance) propagation. It turns out to be such that at each moment of time there is a region in which the exact solution of the equation is identically equal to zero, i.e., heat (substance) propagates with a finite speed.