Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction - Durante, T.; Mel’‎nyk, T. A. (Журнал математичної фізики, аналізу, геометрії, 2007)
We consider an initial boundary value problem for the heat equation in a plane two-level junction Ω_ε which is the union of a domain and a large number 2N of thin rods with the variable thickness of order ε=O(N^-1). The thin rods are divided into two levels depending on boundary conditions given on their sides. In addition, the boundary conditions depend on the parameters α1 and β1, and the thin rods from each level are ε-periodically alternated. The asymptotic analysis of this problem for different values of α and β is made as ε→ 0. The leading terms of the asymptotic expansion for the solution are constructed, the asymptotic estimate in the Sobolev space L^2(0,T;H^1(Ω_ε)) is obtained and the convergence theorem is proved with minimal conditions for the right-hand sides. Mathematics Subject Classification: 35B27, 74K30, 35K20, 35B40, 35C20.