Analysis of the stability of stationary technological transfer processes in the oil-gas and mechanical engineering areas of production

Abstract

The work examines the imitation analogue of the degenerating differential equation that arising from the study of continuous Markov processes in stationary systems closely connected to mathematical models of oil- gas processes in mechanical engineering production. The study of the classes of such equations is associated with the diffusion processes of many areas of mechanical engineering and industrial production, in the case when under approach at the boundary of the domain changes of spatial variable weight coefficient of the equation tends to zero. This means degeneration of the equation, and in applications it is a change in the nature of the diffusion process near the boundary: there is a need to change the technological process and, as a result, changes in production engineering. The solution to the equation is considered in a function class with values in the Hilbert space. A priori estimates of the solution in the spaces of abstract functions at semi-infinite interval have been obtained. A priori estimates of the solution of the Dirichlet problem has been proved. Under certain conditions on the nature of degeneration is established the uniqueness solution to this problem. An effective algorithm has been developed, on the basis of which a computer program has been formed for numerical analysis of the problem. The results are used to automation mechanical engineering production at computation and simulation modeling of diffusion processes, as well as in the formation of a complex of technological operations of production.