A priori estimates for a singular limit approximation of the constitutive laws for chiral media in the time domain

The equations for the evolution of electromagnetic fields in chiral media, in the time domain, are nonlocal in time. In this work we study the validity of a singular limit (local in time) approximation for these nonlocal in time equations, by estimating the size of the difference of the fields as predicted by both models. In particular, we establish an a priori estimate for this difference, depending on the time horizon, properties of the domain, spatial properties of the initial data and the source terms and the chirality measure β of the approximating model.