Starkov P. "Operator approach to transmission problems"

Dissertation work is devoted to the study of transmission problems. A new operator method of the study of transmission problems, which allows all problems to take to the single kind problem, was offered in the work. The abstract transmission problems, which summarize the transmission problems for the Helmholtz equalization, were studied. An abstract two-parameter operator pencil was investigated, one of parameters is considered fixed, and second – spectral. With the use of abstract results of the second and third parts of work the transmission problems for common elliptic equalizations, equalizations of linear theory of resiliency (the Lame equations) and, new interior problem of linear hydrodynamics (the Stoks equations) were investigated. On the basis of the method used in spectral problems, initial-boundary problems were studied.