Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Solution of the Carleman System Using Group Analysis

Author(s):

Sergei Anatolievich Dukhnovsky

Moscow State University of Civil Engineering
Institute of Digital Technologies and Modeling in Construction
Candidate of Physico-Mathematical Sciences

sergeidukhnvskijj@rambler.ru

Abstract:

In this paper, we consider the discrete kinetic Carleman system. The Carleman system is the Boltzmann kinetic equation, and for this model momentum and energy are not conserved. Using group analysis methods, we obtain a solution representing the density of gas particles in a certain area. This limitation is due to the non-negativity of solution. Similarly, it is possible to find exact solutions for other kinetic models.

Keywords

• Carleman system
• group analysis
• invariant solution

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