Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section

In this work, we focus on the time-domain simulation of the propagation of electromagnetic waves in non-homogeneous lossy coaxial cables. The full 3D Maxwell equations, that described the propagation of current and electric potential in such cables, are classically not tackled directly, but instead a 1D scalar model known as the telegraphist's model is used. We aim at justifying, by means of asymptotic analysis, a time-domain "homogenized" telegraphist's model. This model, which includes a nonlocal in time operator, is obtained via asymptotic analysis, for a lossy coaxial cable whose cross section is not homogeneous.