We consider a Dirichlet problem for the Poisson equation in an unbounded period- ically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter , and the level of anisotropy of the cell is determined by a diagonal matrix with positive diagonal entries. The relative size of each periodic perforation is instead determined by a positive parameter . For a given value ̃ of , we analyze the behavior of the unique solution of the problem as (, , ) tends to (0, 0, ̃ ) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.

We consider a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ, and the level of anisotropy of the cell is determined by a diagonal matrix γ with positive diagonal entries. The relative size of each periodic perforation is instead determined by a positive parameter ε. For a given value (Formula presented.) of γ, we analyze the behavior of the unique solution of the problem as (δ, ε, γ) tends to (0,0 Formula presented.) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.

Two-parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach

Musolino P.
2018

Abstract

We consider a Dirichlet problem for the Poisson equation in an unbounded period- ically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter , and the level of anisotropy of the cell is determined by a diagonal matrix with positive diagonal entries. The relative size of each periodic perforation is instead determined by a positive parameter . For a given value ̃ of , we analyze the behavior of the unique solution of the problem as (, , ) tends to (0, 0, ̃ ) by an approach which is alternative to that of asymptotic expansions and of classical homogenization theory.
File in questo prodotto:
File Dimensione Formato  
asydirpoiper06ott17_mn_revision.pdf

non disponibili

Dimensione 355.67 kB
Formato Adobe PDF
355.67 kB Adobe PDF   Visualizza/Apri

I documenti in ARCA 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/10278/3723502
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact