The Spectral Distribution of the Transport Operator with Periodic Boundary Condition in Slab Geometry
WU Hong-xin · Journal of Shangrao Normal University · 2014
The objective of this paper is to research transport equation with nonhomogeneous with periodic boundary condition in slab geometry in Lp(1≤p ∞) space. It proves that the transport operator AHgenerates a C0 semigroup and the second-order remained term of the semigroup is compact and weakly compact,and gets the spectra of the transport operator,only,consist of finite isolated eigenvalues which have a finite algebraic multiplicity in tripΓ. The paper relies on the theory of operators and semigroup methods.