An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170)proposed an alternating iterative method for solving Cauchyproblems for general strongly elliptic and formally self-adjointsystems. However, in many applied problems, operators appearthat do not satisfy these requirements, e.g. Helmholtz-typeoperators. Therefore, in this study, an alternating procedurefor solving Cauchy problems for self-adjoint non-coercive ellipticoperators of second order is presented. A convergence proofof this procedure is given.