Solution of the model problem of heat conduction with Bessel operator

Abstract

In this work, a model boundary value problem for a parabolic equation with a Bessel operator was investigated. The solution to the problem under consideration is sought as a sum of thermal potentials: the double-layer and volume potentials, which reduces the problem to a Volterra integral equation of the second kind. The questions of existence and uniqueness of the obtained integral equation were investigated. The existence condition for the solution to the given problem was found. It is shown that if this condition is fulfilled, the problem has a single solution. The problem considered in this paper is called a model problem because the region in which the solution of the problem is sought is cylindrical and its results will be used in solving boundary value problems for the parabolic equation in noncylindrical regions having different order of degeneracy of the solution region to a point at the initial moment of time.