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Доповіді НАН України. – 2008. – N 9. – С. 16–22.
Асимптотический анализ краевых задач в густых каскадных соединениях
Т.А. Мельник, Г.А. Чечкин
Abstract
We consider the homogenization problem in a singularly perturbed two-dimensional
domain of a new type, which consists of a body of junction and a great number of
alternating thin rods belonging to two classes. Under the assumption that one class
consists of rods of finite length and the other consists of rods of small length and
inhomogeneous Fourier boundary conditions (boundary conditions of the third type)
with perturbed coefficients are set on the boundaries of thin rods, we prove the
homogenization theorems and the convergence of the energy integrals.
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