2010/09/03 by Ferruccio Colombini, Colombini, Ferruccio, Vesselin Petkov +3
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35L45 #msc:35P25 #msc:35Q61
paper · pdf · doi:10.48550/arxiv.1009.0564
arxiv created 2010/11/17 · arxiv updated 2010/11/18
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 → +∞. 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 are invisible in scattering theory.