Building of Mathematical Models of Continuum Media on the Basis of the Invariance Principle

V. O. Bytev
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V. O. Bytev: Krasnoyarsk State University

A chapter in Symmetries of Partial Differential Equations, 1989, pp 329-354 from Springer

Abstract: Abstract The system of differential equations which describes the motion of continuum media of gas, liquid, Reiner-Rievling-type liquid, etc., is considered. $$ \begin{gathered} {\rho_t} + div(\rho u) = 0; \hfill \\ \rho [{u_t} + (u \cdot \nabla )u] - div\Pi (\nabla u) + \nabla \rho; \hfill \\ {\rho_t} + u \cdot \nabla \rho + G\, div\,u + H\phi = 0. \hfill \\ \end{gathered} $$ Solving the problem of its group classification, we obtained all the state equations which lead to the expansion of the main group Γ0 assumed by the initial equations under the arbitrary elements Π, G, H.

Keywords: Group classification; invariance; state equations; internal energy; entropy; pressure; density; stress tensor; continuum media (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-94-009-1948-8_11

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