In this paper we consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω0 and a large number 2N of thin rods with variable thickness of order ε = O(Nì−1). The thin rods are divided into two levels depending on their lenght. In addition, the thin rods from each level are ε−periodically alternated. We investigate the asymptotic behaviour of the solution as ε → 0 under the Robin conditions on the boundaries of the thin rods. By using some special extension operators, the convergence theorem is proved.

Homogenization of a Poisson boundary value problem in a plane thick two-level junction

Perugia C.
2005

Abstract

In this paper we consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωε, which is the union of a domain Ω0 and a large number 2N of thin rods with variable thickness of order ε = O(Nì−1). The thin rods are divided into two levels depending on their lenght. In addition, the thin rods from each level are ε−periodically alternated. We investigate the asymptotic behaviour of the solution as ε → 0 under the Robin conditions on the boundaries of the thin rods. By using some special extension operators, the convergence theorem is proved.
Homogenization; Extension operators; Thick multi-structure.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12070/7022
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