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 an abstract evolutionary system defined on a Hilbert space. In this paper we discuss general framework for homogenization (periodic stochastic) such systems. The method combines unified space approach to systems with operator theoretic reformulation well-established periodic unfolding homogenization. Regarding latter, introduce well-structured family unitary operators that allows describe analyze rapidly oscillating (possibly random) coefficients. We illustrate by establishing stochastic results elliptic equations, Maxwell’s wave equation.