Generalized potentials and their application in solving problems of mathematical physics

We introduce the concept of potential for bounded bodies. We construct the potentials for a two-dimensional semi-infinite region. We solve the problems of determining the nonsteady state temperature fields in a semi-infinite plate with a straight-line cut situated perpendicularly to the boundary of the region under boundary conditions of the first or second kind on the boundary of the region and the edges of the cut.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 28, 1988, pp. 52–58.