Fundamentals of the Mathematical Theory of the Boundary Layer

The book contains the first presentation of the theory of the boundary layer from the standpoint of the theory of differential equations. It presents a new approach to the concepts of the asymptotic series and the pseudo-analytic function. The boundary layer is represented as a pseudoanalytic function. The new approach based on the method of regularization of singular perturbations made it possible to formulate a criterion for the correctness of the mathematical description of the boundary layer and to develop a regular theory for singularly perturbed problems. The book is intended for mathematicians, specialists in aerodynamics and hydrodynamics, physicists, applied mathematicians and engineers who have to deal with problems describing the motion of a viscous flow and with rigid systems of differential equations.