Abstract
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.
Acknowledgments
The author is grateful to Professor M. Mokhtar-Kharroubi for bringing Sahni and Sjörstrand's article (1998) to his attention. This work also benefited from his valuable suggestions and comments. Moreover, the author is indebted to the referees for useful remarks and suggestions.