Mathematical models of many applied problems lead to the need to solve interiorboundary value problems for partial differential equations. The problem under study belongs to the class of ill-posed problems in mathematical physics. The issue of small denominators arises; the existence and uniqueness of the solution depend on the numerical properties of the problem data. Theorems on the uniqueness of the solution and its conditional stability on the well-posedness set are proven, a priori estimates for the solution are obtained, and approximate solutions are constructed using the regularization method. The development of approximate methods for their solution is based on the construction and analysis of numerical methods for solving problems with interior and boundary data for the basic (fundamental, model) equations of mathematical physics.