Publisher DOI: 10.3233/ASY-201654
arXiv ID: 1905.02945
Title: Two-scale homogenization of abstract linear time-dependent PDEs
Language: English
Authors: Neukamm, Stefan 
Varga, Mario 
Waurick, Marcus 
Keywords: abstract evolutionary equations;Maxwell's equations;Periodic and stochastic homogenization;unfolding
Issue Date: 2021
Source: Asymptotic Analysis 125 (3-4): 247-287 (2021)
Abstract (english): 
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework for homogenization (periodic and stochastic) of such systems. The method combines a unified Hilbert space approach to evolutionary systems with an operator theoretic reformulation of the well-established periodic unfolding method in homogenization. Regarding the latter, we introduce a well-structured family of unitary operators on a Hilbert space that allows to describe and analyze differential operators with rapidly oscillating (possibly random) coefficients. We illustrate the approach by establishing periodic and stochastic homogenization results for elliptic partial differential equations, Maxwell's equations, and the wave equation.
ISSN: 0921-7134
Institute: Mathematik E-10 
Document Type: Article
Journal: Asymptotic analysis 
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