Nonlocal homogenisation theory for curl‐div‐systems

We study the curl-div-system with variable coefficients and a nonlocal homogenisation problem associated it. Using, in part refining, techniques from H-convergence for closed Hilbert complexes, we define appropriate topology possibly non-periodic curl-div systems to model highly oscillatory behaviour of on small scales. address under various boundary conditions analyse limit ratio scale over large tending zero. Already standard Dirichlet local system is nontrivial unexpected. Furthermore, provide an analysis impedance type relevant scattering theory Maxwell's equations relate abstract findings weak*-convergence coefficients.