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On the rate of convergence of solutions in domain with periodic multilevel oscillating boundary

✍ Scribed by G. A. Chechkin; C. D'Apice; U. De Maio

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
335 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

In this paper we deal with the homogenization problem for the Poisson equation in a singularly perturbed domain with multilevel periodically oscillating boundary. This domain consists of the body, a large number of thin cylinders joining to the body through the thin transmission zone with rapidly oscillating boundary. Inhomogeneous Fourier boundary conditions with perturbed coefficients are set on the boundaries of the thin cylinders and on the boundary of the transmission zone. We prove the homogenization theorems and derive the estimates for the convergence of the solutions.

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