# On the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditions

Abstract (Summary)

This dissertation is devoted to investigating the time dependent neutron transport equations with reflecting boundary conditions. Two typical geometries --- slab geometry and spherical geometry --- are considered in the setting of L^p including L^1. Some aspects of the spectral properties of the transport operator A and the strongly continuous semigroup T(t) generated by A are studied. It is shown under fairly general assumptions that the accumulation points of { m Pas}(A):=sigma (A) cap { lambda :{ m Re}lambda > -lambda^{ast} }, if they exist, could only appear on the line { m Re}lambda =-lambda^{ast}, where lambda^{ast} is the essential infimum of the total collision frequency. The spectrum of T(t) outside the disk {lambda : |lambda| leq exp (-lambda^{ast} t)} consists of isolated eigenvalues of T(t) with finite algebraic multiplicity, and the accumulation points of sigma (T(t)) igcap{ lambda : |lambda| > exp (-lambda^{ast} t)}, if they exist, could only appear on the circle {lambda :|lambda| =exp (-lambda^{ast} t)}. Consequently, the asymptotic behavior of the time dependent solution is obtained.
Bibliographical Information:

Advisor:Dr. Peter Haskell; Dr. Werner Kohler; Dr. Martin Klaus; Dr. George Hagedorn; Dr. William Greenberg

School:Virginia Polytechnic Institute and State University

School Location:USA - Virginia

Source Type:Master's Thesis

Keywords:mathematics

ISBN:

Date of Publication:03/17/2000