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Symmetry properties of dynamics of two-phase medium

Name
Aleksandr
Surname
Panov
Scientific organization
Chelyabinsk State University
Academic degree
PhD
Position
researcher
Scientific discipline
Mathematics & Mechanics
Topic
Symmetry properties of dynamics of two-phase medium
Abstract
There is considered a system of partial differential equations, which describes dynamics of two-phase medium. Algebra Lie of symmetry group of this system is found. Invariant and partially invariant solutions are found by using symmetry group. Some of solutions describes mixing phases in one- and three-dimensional space.
Keywords
two-phase medium, invariant solutions, symmetry group, partially invariant submodels, Lie algebra
Summary

There is considered a system of partial differential equations, which describes dynamics of interpenetrating movement of two compressible mediums. This system is investigated using methods of group analysis: symmetry groups, invariant solutions, optimal system of subalgebras. Research gave the following results. Algebra Lie of symmetry group is found. Invariant and partially invariant solutions of this system are found. Some of solutions describes mixing phases in one- and three-dimensional space.