On the unbounded solution of the integral equation formulation of the mixed boundary problem

Abstract

This paper presents a modification of the method of singular integral equation formulations for mixed boundary problems, proposed by Cherskij Yu. J. Cherskij [Sov. Math., Dokl. 2, 1173-1176 (1961); translation from Dokl. Adkad. Nauk SSSR 140, 69-72 (1961)]. This modification enables us to treat unbounded solutions of such problems, which are of a great physical interest. This is illustrated by means of a typical problem. As in the case in the Cherskij procedures, the problem is reduced to an infinite algebraic system of equations. The justification of the truncation of such a system has been established.