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Group analysis of a one-dimensional kinetic equation and the moment system closure problem. From invariant relations condition to the group stratification methodстатья
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 4 марта 2026 г.
- Авторы: Borovskikh A.V., Platonova K.S.
- Журнал: Theoretical and Mathematical Physics
- Том: 226
- Номер: 1
- Год издания: 2026
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 132
- Последняя страница: 176
- DOI: 10.1134/S0040577926010095
- Аннотация: We address the question of establishing a relationship between kinetic equations and continuous medium equations based on group analysis methods for differential equations. Continuing our previous studies, we consider the simplest one-dimensional case. We examine equations with a submaximal (three-dimensional) symmetry group. It turns out that the presence of an external force field requires a radical revision of the problem setting, not only in terms of the use of group methods, but also in the general context. Namely,it turns out that it is impossible to consider the continuous medium equations as a reduced system ofmoment equations, since, generally speaking, there are merely no high-order moments (in our case, oforders greater than one). However, the use of group methods allows us to overcome this crisis situation(from the point of view of widely held beliefs) by passing to an actually equivalent setting of the problem, which affects neither the moment system nor the nonexisting moment variables. The problem setting transformed in this way turned out, on the one hand, to be related to the well-known group stratification method, somewhat expanding the very understanding of this method, and, on the other hand, providing a simple and effective general method for solving the problem of the relationship between kinetic equations and continuum medium equations.
- Добавил в систему: Боровских Алексей Владиславович
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