The direct electromagnetic scattering problem from an imperfectly conducting cylinder at oblique incidence (Q713442)

Maxwell's equations are considered in the exterior of the cylinder \(D\times\mathbb{R}\) with \(D\subseteq\mathbb{R}^{2}\) a domain having \(C^{2}\)-boundary. The material is assumed to be isotropic, inhomogeneous and constant in the third coordinate direction and the electromagnetic field is assumed to be of the form \[ \left(E,H\right)\left(t,x,y,z\right)=\left(e,h\right)\left(x,y\right)\exp\left(-\imath\left(\omega t+\beta z\right)\right). \] On the boundary, the Leontovich impedance boundary condition is imposed. This allows to reduce the system to an exterior boundary value problem for an elliptic second order system in the third components of \(e\) and \(h\). Well-posedness of this system is shown based on results in the framework of the so-called Lax-Phillips method, which reduces the solvability of the exterior domain problem to a bounded domain problem.