Marco Marletta (Cardiff University)
Essential spectra and spectral pollution for inhomogeneous, anisotropic dissipative Maxwell
and Drude-Lorentz systems
Abstract:
Abstract: The methods required to study spectral pollution for dissipative
Maxwell (and related) systems turn out to be closely connected to the methods
required to study the essential spectrum for such systems. These are very
different from the methods used for Schrödinger equations: in particular,
the presence of dissipation - e.g. in the form of conductivity - means that the
essential spectrum can be changed by changing the coefficients in the system on
any arbitrarily small, non-empty open set. Our methods use instead a reduction
of the system to a triangular block operator matrix, together with the concept
of limiting essential spectrum developed by Sabine Boegli in 2015. We are able
to show that any spectral pollution is confined either to the real axis or to a
segment of the imaginary axis: any computed eigenvalue whose real and imaginary
parts are both non-zero is genuine.