Реферат: The foundations of group analysis of differential equations were laid by S. Lie. This theory was essentially developed in works of L. V. Ovsiannikov, N. H. Ibragimov, their students, and followers. Notion of the partially invariant solution to the system of differential equations (Ovsiannikov 1964) substantially extended possibilities of exact solutions construction for multidimensional systems of differential equations admitting the Lie group. It is important to note that fundamental equations of continuum mechanics and physics fall in this class a priori as invariance principle of space, time, and moving medium there with respect to some group (Galilei, Lorenz, and others) are situated in the base of their derivation. It should be noticed that classical group analysis of differential equations has a local character. To apply this approach to initial boundary value problems, one need to provide the invariance properties of initial and boundary conditions. Author (1973) studied these properties for free boundary problems to the Navier–Stokes equations. Present chapter contains an example of partially invariant solution of these equations describing the motion of a rotating layer bounded by free surfaces.

Библиографическая ссылка: Pukhnachev V.V.
Partial Invariance and Problems with Free Boundaries
Глава монографии Symmetries and Applications of Differential Equations. In Memory of Nail H. Ibragimov (1939–2018). – Springer., 2021. – C.251–267. DOI: 10.1007/978-981-16-4683-6_9 Scopus РИНЦ OpenAlex

Идентификаторы БД:

Scopus:	2-s2.0-85121729746
РИНЦ:	47550179
OpenAlex:	W4205629151

Цитирование в БД: Пока нет цитирований

Альметрики: