WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 15, 2016
The Spectrum Distribution of Transport Operator with Abstract Boundary Conditions in Slab Geometry
Authors: , ,
Abstract: n 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 − BH)−1K ∥ (|Imλ| → +∞) is bounded in the trip Γε, and the spectrum of transport operator AH consists of only finite isolated eigenvalues with a finite algebraic multiplicities in trip Γε. The main methods rely on operators theory, resolvent operators and comparison operators approach.