The Spectral Analysis Of The Transport Operator With General Boundary Condition In Slab Geometry

In this paper, we investigate one type of transport equation with general boundary conditions in slab geometry by the methods of modern analysis, such as functional analysis , the theory of operator and the theory of semigroup. We have got a series of new results about the spectrum of the transport operator relating to the transport equations. The main results are showed below:1. We discuss anisotropic, monoenergy, homogeneous transport operator A with general boundary operator in slab geometry. We prove that the operator A generates a C₀ semigroup and the second remainder of the C₀ semigroup is compact in L^p(11 space.2. We discuss anisotropic, continuous energy, homogeneous transport operator A with general boundary operator in slab geometry. We prove that the operator A generates a C₀ semigroup and the second remainder of the C₀ semigroup is compact in L^p(l1 space.3. We investigate these two types of operators above and prove that the operators A have only finite, finite algebraic multiplicity, isolated eigenvalues. Also we prove that the existence of the dominant eigenvalue.