E.V. Lisovsky1, O.V. Druzhinina2

1 Kaluga branch of the Bauman Moscow State Technical University (Moscow, Russia)

2 Federal Research Center «Computer Science and Control» of Russian Academy of Sciences (Moscow, Russia)

Many processes of natural science and technology are modeled by nonlinear systems of equations with distributed parameters. The class of models defined using Burgers equations, as well as its generalizations and modifications, is of theoretical and applied interest. It is known that models of this class are used for the mathematical description of the motion of liquid and gas, the phenomena of turbulence, as well as for the mathematical description of waves in a dissipative medium, the processes of nonlinear acoustics and cosmology, and the features of the traffic flow. The development of methods for studying the stability of equilibrium states of this class of models is an urgent direction. One of the effective approaches to the analysis of the stability of such systems is an approach based on both the generalized direct Lyapunov method and mathematical modeling using abstract evolutionary equations. The aim of the paper is to develop an approach to the analysis of the qualitative behavior of solutions for turbulence models in a multiphase medium. The characteristics of the main directions of research of the Burgers equation and some of its generalizations are given. A class of models with distributed parameters is studied based on the method of mathematical modeling using abstract evolutionary equations. An approach to the analysis of the stability of equilibrium states for the modified Burgers model in the case of a two-velocity medium is considered. To obtain sufficient conditionss of stability, the transition to linearized equations and the direct Lyapunov method were used. The results can find application in solving problems of modeling and stability of nonlinear dynamic systems with distributed parameters.

Druzhinina O. V., Lisovsky E. V. Stability analysis of equilibrium states of a nonlinear models with distributed parameters.

Nonlinear World. 2021. V. 19. № 4. 2021. P. 50−59. DOI: https://doi.org/10.18127/j20700970-202104-06 (In Russian)

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