Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review
Partial Invariance and Problems with Free Boundaries. / Pukhnachev, V. V.
Nonlinear Physical Science. ed. / Albert C. J. Luo; Rafail K. Gazizov. 1. ed. Springer Science and Business Media Deutschland GmbH, 2021. p. 251-267 (Nonlinear Physical Science).Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review
}
TY - CHAP
T1 - Partial Invariance and Problems with Free Boundaries
AU - Pukhnachev, V. V.
N1 - Publisher Copyright: © 2021, Higher Education Press.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85121729746&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/13b489a0-aa02-379d-a8a8-7a101654f41f/
U2 - 10.1007/978-981-16-4683-6_9
DO - 10.1007/978-981-16-4683-6_9
M3 - Chapter
AN - SCOPUS:85121729746
SN - 978-981-16-4682-9
SN - 978-981-16-4685-0
T3 - Nonlinear Physical Science
SP - 251
EP - 267
BT - Nonlinear Physical Science
A2 - Luo, Albert C. J.
A2 - Gazizov, Rafail K.
PB - Springer Science and Business Media Deutschland GmbH
ER -
ID: 35196584