Asymptotic Behaviour of the Energy Integral of a Two-Parameter Homogenization Problem with Nonlinear Periodic Robin Boundary Conditions

We consider a nonlinear Robin 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. The relative size of each periodic perforation is determined by a positive parameter...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2019-11, Vol.62 (4), p.985-1016
Main Authors: de Cristoforis, Massimo Lanza, Musolino, Paolo
Format: Article
Language:English
Subjects:
Asymptotic properties
Asymptotic series
Boundary conditions
Homogenization
Integrals
Parameters
Perforation
Periodic structures
Poisson equation
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Summary:We consider a nonlinear Robin 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. The relative size of each periodic perforation is determined by a positive parameter ε. Under suitable assumptions, such a problem admits a family of solutions which depends on ε and δ. We analyse the behaviour the energy integral of such a family as (ε, δ) tends to (0, 0) by an approach that represents an alternative to asymptotic expansions and classical homogenization theory.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091518000858