The property of a finite speed of a perturbation distribution to the Cauchy problem
for non-divergence form of the parabolic equation based on comparison method and asymptotic
behavior of a self-similar solution is achieved. Defined the conditions for the availability of blow-ups
and global solutions to a given problem using Hopf’s maximum principle for the parabolic equation in
non-homogeneous medium not in divergence form. The resulting asymptotics has been used as an
initial approximation and numerical solutions have been calculated.