Karpalyuk T. Symmetry classification of nonlinear convection-diffusion equations in the case of Galilean algebras

The thesis focuses on the research of symmetry properties of systems of nonlinear convection-diffusion and reaction-convection-diffusion equations. Nonlinear systems of reaction-convection-diffusion equations, which are invariant in respect to a Galilean algebra and some extensions of this algebra with scale and projective operators, were established up to groups of local continuous equivalence transformation of the systems. Two-dimensional systems of convection-diffusion equations, which are invariant with respect to a generalized Galilean algebra at a two- and three-dimensional vector field U, were found. Also one-dimensional systems of convection-diffusion equations at ?R^3, which are invariant with respect to a Galilean algebra, extended by scale and projective operators, were detected. Some three-component systems of convection-diffusion equations, which are invariant in respect to generalized Galilean algebras, were generalized to systems, which are analogues of the Navier-Stokes system at n?m, still keeping invariance of the received systems in respect of the same algebras.