Aperiodic electromagnetic waves in exterior domains
The paper considers the vectorial wave equation with the electric and magnetic boundary conditions, respectively, corresponding to the assumption of total reflection, in an exterior domain assuming a time- harmonic forcing term of frequency \(\omega\). Main result is that the solution U behaves for large time t like \[ U(t)=tP_{+0}(U_ t(0)- i\omega^{-1}F)+P_{+0}(U(0)+\omega^{-2}F)+o(1)\quad as\quad t\to \infty, \] where \(P_{+0}\) denotes the projection on the null space of the selfadjoint realization of the Laplacian with the above boundary conditions. The result rests on the low frequency behaviour of the related time-harmonic problem. The result is applied to obtain the corresponding asymptotic properties of the solution of the isotropic homogeneous Maxwell's equations.
electric and magnetic boundary conditions
isotropic homogeneous Maxwell's equations
scientific article; zbMATH DE number 4105468
scientific article