nonlinear problems

A mathematical model for propagation of a small disturbance in the moving gas of a long pipeline has been built in the paper. The model contains two coupled equations, the coefficients of which are expressed via the parameters of the initial process --- mass density and mass flow rate.  In the frame of the model, the influence of parameters of the initial stationary gas flow on propagation of the pulses initiated by a local fluctuation, originated in the stream, was studied numerically.

The problem of parameters identification of the bursts of the medium conductivity coefficient according to the tomography of the applied quasipotentials is considered. The method of image reconstruction is suggested, according to which the problem of analysis is reduced to the application of numerical methods of quasiconformal mappings, and the problem of synthesis is reduced to the solving the problem of parametric identification. The results of numerical experiments are presented and their analysis is carried out.