The Spectrum Distribution of Transport Operator with Abstract Boundary Conditions in Slab Geometry

摘要

In this paper, transport equation with continuous energy, nonhomogeneous medium and abstract boundary conditions is studied in slab geometry. It is to prove that |Imλ| ‖ K(λI - B_H)~(-1) K ‖ (|Imλ| → + ∞) is bounded in the trip Γ_ε, and the spectrum of transport operator A_H consists of only finite isolated eigenvalues with a finite algebraic multiplicities in trip Γ_ε. The main methods rely on operators theory, resolvent operators and comparison operators approach.