Green's contact functions for heat conduction of two half-spaces and half-planes with application to several boundary contact problems

Green's contact functions are constructed for two half-spaces and two half-planes for materials with different thermal conductivities. With the aid of these contact functions some bimetal problems are reduced to boundary integral equations along the outer boundary where only the boundary conditions are to be satisfied. The boundary integral operators are investigated in the plane case. They are Fredholm operators with index zero. The asymptotics of the density of the potentials, which depends on the material parameters and on the angles between the contact line and the outer boundary, is determined by the Mellin transform technique.