Mel'nyk T. Asymptotic methods for solving of spectral problems and boundary value problems in domains with singular perturbed boundaries

The thesis deals with development of asymptotic methods for investigation of spectral and boundary value problems in thick singular degenerated junctions of different types and in thin perforated domains with rapidly varying thickness. Using proposed methods, the asymptotic behaviour of eigenvalues, eigenfunctions and solutions of boundary value problems is studied, the leading terms of asymptotics are constructed, and asymptotic estimates are proved. The influence of boundary conditions, geometric configuration of a such domains, density and rigidity of the domain materials on the asymptotic behaviour is investigated.