Homogenization of an alternating Robin-Neumann boundary condition via time-periodic unfolding
type: Item
instance of: scholarly article
title: Homogenization of an alternating Robin-Neumann boundary condition via time-periodic unfolding
zbMATH Open document ID: 1370.35034
author: Micol Amar
author: Daniele Andreucci
author: Dario Bellaveglia
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2017-03-17T00:00:00Z
review text: In this paper the authors deal with a problem of homogenization of a parabolic equation, where the coefficients are oscillating, in space and in time, in a domain with holes. Two type of behaviors are considered respect to the suitable balance between the space and time oscillations. Let \(\tau\) and \(\varepsilon\) be the time and space period of oscillations respectively, the authors consider the fast oscillations in time when \(\tau\theta_\tau / \varepsilon \leq C\) and the case of slow oscillation in time when \(\tau\theta_\tau / \varepsilon \) goes to \(+\infty\), where \(\theta_\tau\) is relate on the degeneracy of the estimate of the time derivative, whose \(L^p\)-norm is assumed to behave in the limit as the parameter \(\theta_\tau\). The Robin-Neumann oscillating boundary conditions allow relevant estimates for homogenization process. In the limit, using unfolding time-periodic techniques, a macroscopic parabolic problem is achieved, which contain an extra linear term due to the absoption determined by the Robin condition.
reviewed by: Marco Codegone
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 6695865
zbMATH Keywords: unfolding technique
zbMATH Keywords: space and time oscillations
MaRDI profile type: Publication
full work available at URL: j.na.2016.05.018
OpenAlex ID: W2466259161
cites work: Homogenization and Two-Scale Convergence
cites work: The time-periodic unfolding operator and applications to parabolic homogenization
cites work: Q4673618
cites work: Q5313738
cites work: Permeability of interfaces with alternating pores in parabolic problems
cites work: A model for enhanced and selective transport through biological membranes with alternating pores
cites work: Q5308190
cites work: The periodic unfolding method in domains with holes
cites work: Periodic unfolding and homogenization
cites work: The Periodic Unfolding Method in Homogenization
cites work: The periodic unfolding method for perforated domains and Neumann sieve models
cites work: Exact internal controllability in performed domains
cites work: The periodic unfolding method in perforated domains
cites work: Q3961204
cites work: Homogenization in open sets with holes
cites work: Homogenization in perforated domains with rapidly pulsing perforations
cites work: Non-homogeneous Neumann problems in domains with small holes
cites work: Q5562267
cites work: Asymptotic expansions in perforated media with a periodic structure
cites work: The general theory of homogenization. A personalized introduction
DOI: 10.1016/J.NA.2016.05.018
description: scientific article; zbMATH DE number 6695865