Klevtsovskyi A. Asymptotic analysis for boundary-value problems in thin domains with a local irregularity

The thesis is devoted to the investigation of linear and semilinear elliptic and parabolic boundary-value problems in thin star-shaped domains consisting of several thin curvilinear cylinders that are joined through a domain (node) of diameter О(ε). Сomplete asymptotic expansions for solutions to linear boundary-value problems and asymptotic approximations for solutions to semilinear boundary-value problems are constructed and justified. For each problem considered in the thesis, the corresponding limit problem on the graph is derived. The asymptotic energetic and uniform pointwise estimates for the difference between the solution to an original problem and the asymptotic approximation for the solution to the limit problem are proved.