Rassokha I. Investigation of symmetry properties of nonlinear systems of parabolic type

The dissertation is devoted to investigation of symmetry properties of nonlinear equations of parabolic type. With accuracy of transformation of equivalence the full group classification of symmetry properties of reaction-convection-diffusion equation was made. For some equations of the given class the descrete symmetriеs and formulae of solutions were found. The conception of Q-conditional equivalence was introduced and the algorithm of finding of the Q-conditional equivalence group was worked out. The appearance of a Galilean algebra and it's extensions in respect to which the system of nonlinear reaction-convection-diffusion equations can be invariant is investigated. The kind of nonlinearities with which this system is invariant in respect to that algebra is determined within continuous equivalence transformations.