| Abstract [eng] |
In this thesis "Asymptotics of a solution to the time-periodic heat equation set in domains with corner points" by Vytenis Šumskas, a time-periodic boundary value problem for the heat equation is considered. It is assumed that the problem is set in a two dimensional domain Omega having a corner point on the boundary. The time-periodic problem was reduced to a sequence of elliptic problems in the domain with a corner point. Asymptotic representations of solutions to these problems were obtained using methods proposed in numerous works of V. Maz’ya, S. Nazarov and B. Plamenevskij. Estimates of asymptotic terms were derived. These estimates together with representations of solutions to elliptic systems were used to determine the time-periodicity of solution to the time-periodic problem in a neighborhood of the corner point of domain Omega. |
