On the spectrum of absorption operators with Maxwell boundary conditions arising in population dynamics and transport theory. A unified treatment.

In this paper we investigate the spectral properties of several (collisionless) transport-like models in 2D-geometry with Maxwell–type boundary conditions. These equations are arising in different fields of applications (nuclear reactor analysis or population dynamics) but they all share the same spectral structure. We explain this by showing that, up to suitable transformations, each of these models reduces to an abstract one-velocity transport equation for which an explicit description of the spectral properties is provided in this paper.