The construction of special explicit solutions of the boundary-layer equations. Unsteady flows

The generalization of the method for determining special explicit solutions of partial differential equations developed by the author (Q. Jl Mech. appl. Math. 47 (1994) 247-260) is used to derive new explicit solutions of the unsteady two-dimensional boundary-layer equations. The method, as applied to a partial differential equation with three independent variables, reduces the equation to an overdetermined system of ordinary differential equations having explicit solutions, and a joining system of partial differential equations with two independent variables which can easily be solved. The solutions produced by the method contain arbitrary functions of space and time variables which are determined for specific problems by a concrete definition of boundary conditions and/or the external flow form. A comparison of the method with group-theoretic methods for finding special solutions of partial differential equations is discussed.