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Registration Number

0215U000472, 0112U002321 , R & D reports

Title

The investigation of Galilei invariance of nonlinear equations systems of mathematical physiscs of evolution type.

Head

Serov Mykola Ivanovych,

Registration Date

25-02-2015

Organization

Polava National Technical University named in the honour of Yuri Kondratyuk

Description

The object of the research is some nonlinear equations of mathematical physics. The aim of the investigation is studying simmetrical properties of certain mathematical models. From all possible models we selected only such ones, which satisfy Galilean relativity principle. For the research we used the method of the group analysis of differential equations.We have got linear representations of Galilean algebras, an extended Galilean algebra, an eneralized Galilean algebra, a Poincare algebra, a conform algebra. The basic group of equivalent transformations of the reaction-convection-diffusion system and its basic invariance algebra were set up. We have found some nonlinearities, at which the system is invariant in respect to a Galilean algebra and its extensions. The basic group of equivalence transformations and the basic invariance algebra of the multi-dimensional convection-diffusion system were studied. We also have detected some nonlinearities, at which the system is invariant in respect to a Galilean algebra, extended and generalized Galilean algebras.

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Блажко Людмила Миколаївна
Омелян Олександр Миколайович
Рассоха Інна Володимирівна
Сєрова Марія Михайлівна