Pochecketa O. Extended group analysis of generalized Burgers equations.

The thesis is devoted to the symmetry analysis of several classes of differential equations, namely of the class of variable-coefficient generalized Burgers equations, the classes of linearizable generalized Burgers equations, the class of generalized potential Burgers equations, the class of generalized Burgers equations in conserved form, the class of variable-coefficient generalized Burgers equations with linear damping and some its subclasses. For all these classes the exhaustive description of their equivalence groupoids is presented by means of determining of the corresponding equivalence group and of the evidence that either the class is normalized or it can be partitioned into two or three normalized subclasses. For the class of variable-coefficient generalized Burgers equations the extended group analysis is provided. The algebraic method is used to solve the group classification problem for this class. Reduction operators, Lie and nonclassical reductions, conservation laws, potential admissible transformations and potential symmetries of equations from this class are exhaustively described. A method of classification of Lie reductions for equations of a normalized class with respect to the equivalence group of this class is proposed. This method %together in~combination with an optimized choice of ansatzes allowed to exhaustively describe hidden symmetries for equations from this class and to construct some new exact solutions of such equations. The problem of group classification is also solved for the class of variable-coefficient generalized Burgers equations with linear damping. Classification results are used to construct exact solutions for equations from this class.