The diffraction of stress waves by a plane finite crack in two dimensions: uniqueness and existence

In this paper we consider the two-dimensional problem of the diffraction of stress waves by a finite plane crack in a homogeneous isotropic elastic solid. We prove that, provided the elastic displacement is bounded, this problem has at most one solution. Also, by introducing a new class of Green functions, we are able to give a constructive proof of existence. The solution is given in terms of the solution of any one of a class of Fredholm integral equations of the second kind.