Plane Potential Field Outside a Symmetric T-Shaped Profile

Abstract

We consider a new plane problem of the potential theory outside a symmetric T-shaped profile. In view of the symmetry of the profile, we reduce the analyzed problem to a mixed boundary-value problem in a half plane with perpendicular cut whose solution is constructed by the method of partial domains with the use of polar coordinates and the Mellin integral transformation. The original problem is reduced to a system of two Wiener–Hopf equations whose solution is reduced to a completely regular infinite system of linear algebraic equations. The solution of the infinite system is approximately found by the method of reduction. The obtained explicit expressions for the unknown harmonic function make it possible to efficiently determine its values for all possible values of the arguments.