Compactness properties for linear transport operators with abstract boundary conditions in slab geometry
Khalid Latrach · Transport Theory and Statistical Physics · 1993
The purpose of this paper is to give a systematic analysis of the compactness for one-dimensional transport equations, with general boundary conditions including all known classical boundary conditions. We give necessary and sufficient conditions for some power of (λ-T)-1 K to be compact where T is the streaming operator and K the scattering operator. We also give necessary conditions for some remainder term Rn(t) of the Dyson-Phillips expansion to be compact. Finally, an open problem is indicated.