Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction
Ключові слова:homogenization, thick junctions, parabolic problems, anisotropic Sobolev spaces.
АнотаціяWe consider an initial boundary value problem for the heat equation in a plane two-level junction We which is the union of a domain and a large number 2N of thin rods with the variable thickness of order e = 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 a ≥ 1 and b ≥ 1, and the thin rods from each level are e-periodically alternated. The asymptotic analysis of this problem for different values of a and b is made as e → 0. The leading terms of the asymptotic expansion for the solution are constructed, the asymptotic estimate in the Sobolev space L2(0; T;H1(We)) is obtained and the convergence theorem is proved with minimal conditions for the right-hand sides.
Mathematics Subject Classification: 35B27, 74K30, 35K20, 35B40, 35C20.
Durante, T.; Mel`nyk, T. Asymptotic Analysis of a Parabolic Problem in a Thick Two-Level Junction. Журн. мат. фіз. анал. геом. 2007, 3, 313-341.
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