In this paper, the approaches to the study of mathematical models of the theory of linear elasticity are developed. The general formulation of the 3-dimensional problem based on the representation of the fundamental solution in the form of V. P.
In the paper, we illuminate the connection between diffusion processes and partial differential equations of parabolic type. The emphasis is on degenerate parabolic equations with real-valued coefficients. These equations are the generalization of the classical Kolmogorov equation of diffusion with inertia, which may be treated as Fokker-Planck-Kolmogorov equations for the corresponding degenerate diffusion processes. A fundamental solution of the Cauchy problem for Fokker-Planck-Kolmogorov equation determines the transition probabilities to the corresponding diffusion process.