  We prove a compactness result related to $G$-convergence for autonomous
evolutionary equations in the sense of Picard. Compared to previous work
related to applications, we do not require any boundedness or regularity of the
underlying spatial domain; nor do we assume any periodicity or ergodicity
assumption on the potentially oscillatory part. In terms of abstract
evolutionary equations, we remove any compactness assumptions of the resolvent
modulo kernel of the spatial operator. To achieve the results, we introduced a
slightly more general class of material laws. As a by-product, we also provide
a criterion for $G$-convergence for time-dependent equations solely in terms of
static equations.
