Incoming and disappearing solutions of Maxwell's equations
Vesselin Petkov ,
(Université Bordeaux I, France)
Jueves 24 de febrero 2011
We prove that in contrast to the free wave equation in R3 there are no incoming solutions of Maxwell?s equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming waves. With their aid, we construct dissipative boundary conditions and solutions to Maxwell?s equations in the exterior of a sphere which decay exponentially as t ! +1. They are asymptotically disappearing. Disappearing solutions which are identically zero for t T > 0 are constructed which satisfy maximal dissipative boundary conditions which depend on time t. Both types of solutions are invisible in scattering theory. This work is in collaboration with F. Colombini and J. Rauch..