$G$-Convergence of Linear Differential Equations

Abstract

We discuss $G$-convergence of linear integro-differential-algebraic equations in Hilbert spaces. We show under which assumptions it is generic for the limit equation to exhibit memory effects. Moreover, we investigate which classes of equations are closed under the process of $G$-convergence. The results have applications to the theory of homogenization. As an example we treat Maxwell's equation with the Drude–Born–Fedorov constitutive relation.