On local singularities in mathematical models of physical fields (Q2714510)

A unique approach of determining the character of singularities in different physical fields is presented. The approach is based on the introduction of a concept of general solution to the boundary value problem. These general solutions allow a complete description of the field around the singularity points. It is shown that the singular solutions provide a reliable decription of the quantative and qualitative characteristics of the field outside a small zone in the singularity neighborhood. The analysis of singular solutions demonstrates the difficulties in interpreting the physical meaning of the solution near the singularities.