Omelyan O. Symmetry properties and exact solutions of nonlinear equations of parabolical type

The systems of nonlinear equations of diffusion and reaction of diffusion which are invariant concerning Galilei Algebras are discovered. For these systems the expansions of Galilei Algebras by operators of scale and projection transfor-mations are investigated. For Galilei invariant system of nonlinear equations of diffusion the Lie's anzatz were constructed and exact solutions were generated. Nonlocal transformations of equivavalence were applied for finding system of nonlinear equations of diffusion which may be linearized and for constructing nonlocal anzatz of nonlinear system of equations of diffusion which may be re-duced to Galilei invariant system by nonlocal transformations of equivalence. With nonlocal transformations of equivalence there were constructed the repro-duction solution nonlocal formulas of diffusion nonlinear equation system which may be linearized by nonlocal transformations of equivalence. The full group classification of symmetries properties of system of nonlinear chemotaxis equa-tions was performed.