On the second boundary value problem for the equation of heat conduction in an unbounded plane angle

Abstract

In the article, the second homogeneous boundary value problem is considered in an infinite angular domain. Solution of the problem is reduced to solving the singular Volterra integral equations of the second kind with kernel whose norm is equal to unity. By the method of Carleman-Vekua, solving the integral equation is reduced to solving the inhomogeneous equation of Abel. The theorem on the existence of a non-trivial solution of the second homogeneous boundary value problem in a non-cylindrical domain is proved. The solution of the given problem is obtained in an explicit form.