We consider a mixed boundary-value problem for a Poisson equation in a plane two-level junction Ωε that is the union of a domain Ω0 and a large number 3N of thin rods with thickness of order ε = O(N −1). The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The homogeneous Dirichlet conditions and inhomogeneous Neumann conditions are given on the sides of the thin rods from the first level and the second level, respectively. Using the method of matched asymptotic expansions and special junction-layer solutions, we construct an asymptotic approximation for the solution and prove the corresponding estimates in the Sobolev space H1(Ωε) as ε →0 (N → +∞).

### Asymptotic approximation for the solution to a boundary-value problem with varying type of boundary conditions in a thick two-level junction.

#### Abstract

We consider a mixed boundary-value problem for a Poisson equation in a plane two-level junction Ωε that is the union of a domain Ω0 and a large number 3N of thin rods with thickness of order ε = O(N −1). The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The homogeneous Dirichlet conditions and inhomogeneous Neumann conditions are given on the sides of the thin rods from the first level and the second level, respectively. Using the method of matched asymptotic expansions and special junction-layer solutions, we construct an asymptotic approximation for the solution and prove the corresponding estimates in the Sobolev space H1(Ωε) as ε →0 (N → +∞).
##### Scheda breve Scheda completa Scheda completa (DC)
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11386/1549925`
##### Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

##### Citazioni
• ND
• 7
• ND