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The News of Altai State University
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Management, Computer Facilities and Computer Science
Mathematics and Mechanics
Mathematics and Mechanics

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E.Yu. Meshcheryakova

Group Analysis of Incompressible Viscoelastic Maxwell Continuum Equations

The researcher considers an incompressible viscoelastic Maxwell continuum with constant relaxation time. The system of equations describing such medium consists of continuity equation, momentum equation and a tensor rheological relation. The author studies the group properties of the model for three records of rheological relation: with Jaumann rotational derivative and with the upper or lower convective derivatives.
First and second order optimal systems of subalgebras are constructed.
Key word: Maxwell incompressible viscoelastic medium, Lie group, optimal system of subalgebras.

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