Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-scale homogenization of abstract linear time-dependent PDEs   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.

24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph