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 Dr. William Greenberg Committee Chair Dr. George Hagedorn Committee Member Dr. Martin Klaus Committee Member Dr. Peter Haskell Committee Member Dr. Werner Kohler 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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