PROBLEMS OF MATHEMATICAL PHYSICS WITH BOUNDARY CONDITIONS INCOMPLETELY DEFINED

摘要

The possibility to construct the analytic solutions of boundary-value problems of mathematical physics for noncanonical domains is important from the viewpoint of the development of efficient algorithms to quantitatively estimate the characteristics of fields under study. The use of the superposition method allows one to analyze a wide class of specific problems applying the introduced notion of the general solution of a boundary-value problem. However, in this case, some difficulties can arise in the construction of calculation algorithms, because the boundary conditions are incompletely defined on the intervals, where the functions appearing in the general solution are orthogonal to one another. We present examples of problems with such difficulties and study their nature and methods to overcome them. The quantitative estimates of the exactness of constructed solutions are given.