Abstract
Paper is devoted to determine the solution of a non-stationary heat equation in an axial symmetry cylindrical coordinates subject to a nonhomogeneous mixed discontinuous boundary conditions of the first and of the second kind inside the disk of an finite surface cylinder. The solution of the given mixed boundary value problem is obtained with the aid of a classical methods and based on the application of a new type of a dual series equations (DSE) with a Bessel function of the first kind of order zero as a kernel. The solution of obtained DSE which is discussed in this paper is introduced to a Fredholm integral equation of the first kind.
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