Vaneeva O. Group classification and nonclassical symmetries of reaction-diffusion equations

The classes of (1+1)-dimensional nonlinear reaction-diffusion and filtration equations are investigated. The aim is development of new group analysis methods and their application to the subject of inquiry. The methods are group theoretical (classical Lie-Ovsiannikov method, modified direct method of finding conservation laws, reduction method et al.). A new group classification method is developed. The application of this method allows us to classify Lie symmetries for classes of nonlinear reaction-diffusion equations with coefficients which depend on spatial variable. As a result the classification problems concerning Lie symmetries, local conservation laws and admissible transformations for the reaction-diffusion equations are solved; potential nonclassical symmetries of fast diffusion equation are classified; nonlinearities for which nonlinear filtration equations admit nontrivial nonclassical symmetries are described. The fields of application are mathematical physics, biology, theoretical physics and chemistry.