Approximate Cloaking for the Full Wave Equation via Change of Variables

We study, in the context of the full wave equation, an approximate cloaking scheme that was previously considered for the Helmholtz equation [R. V. Kohn, D. Onofrei, M. S. Vogelius, and M. I. Weinstein, Comm. Pure Appl. Math., 63 (2010), pp. 973--1016, H.-M. Nguyen and M. S. Vogelius, Arch. Ration. Mech. Anal., 203 (2011), pp. 769--807]. This cloaking scheme consists in a combination of an absorbing layer with an anisotropic layer, obtained by so-called transformation optics. We give optimal bounds for the visibility that tend to zero as a certain regularization parameter approaches 0. Our bounds are based on recent estimates for the Helmholtz equation [from Nguyen and Vogelius], some low frequency improvements of these estimates, and the use of Fourier transformation in time. Read More: http://epubs.siam.org/doi/abs/10.1137/110833154