## F V V Vj J

We can obtain the system of equations for defining the quantities i'i*, V3*. ■ • ■ by summing up the equations of the principal subsystem for the plane boundary layer and the auxiliary subsystem for the antiplane boundary layer up to the quantities 0(tj1):

A10 df,

The quantities X" P^' are found from the formulas 38.12.

We will treat the first and third conditions 45.3 as the boundary conditions for the plane boundary layer i'u + i'i,o + f7,0'u = 0 «'3* + ^'"<'3,0 + rf*'Cvyi + 7]SC2V3.2 = 0.

We represent the plane boundary layer as a sum of the symmetric (corresponding to the bending of the half-band) and the antisymmetric (corresponding to the extension of the half-band) parts of the plane boundary layer.

For the antisymmetric part the boundary conditions will be written as

Since the problem is linear, we can represent the solution of equations 45.4 with the edge conditions 45.5 and the homogeneous conditions on the faces as a linear combination of three problems with the following conditions at the edge = 0:

THE INTERNAL ELECTRO FAA STIC STATE A NO THE HOUNDA R )' ¡A Y ER 213

We solve problems 1 and II by integrating the system of equations of the plane problem with the nonhomogeneous conditions 1 and II. We solve problem III by integrating the nonhomogeneous equations 45.4 with the homogeneous conditions III. We multiply the solutions of I—III by the factors

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