Title page for ETD etd-03072000-23200015


Type of Document Dissertation
Author Song, Degong
Author's Email Address dsong@vt.edu
URN etd-03072000-23200015
Title On the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditions
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Greenberg, William Committee Chair
Hagedorn, George A. Committee Member
Haskell, Peter E. Committee Member
Klaus, Martin Committee Member
Kohler, Werner E. Committee Member
Keywords
  • transport equation
  • spectrum
  • stability
  • strongly continuous semigroup
Date of Defense 2000-02-14
Availability unrestricted
Abstract
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.

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