Problems of heat conduction with different boundary conditions in noncylindrical domains

In a degenerating domain homogeneous problems for the heat equation with different boundary conditions are considered. Problems are reduced to singular integral equations with incompressible kernels. Also in an infinite dihedral angle, the first boundary value problem for the equation of heat conduction is considered. The problem is reduced to a one-dimensional problem, the corresponding homogeneous problem of which is reduced to the singular integral Volterra that was considered above.