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 AbstractThis dissertation is devoted to investigating the time dependent neutron transportequations with reflecting boundary conditions. Two typical geometries --- slab geometry

and spherical geometry --- are considered in the setting of

L^pincludingL^1. Someaspects of the spectral properties of the transport operator

Aand the stronglycontinuous semigroup

T(t)generated byAare studied. It is shown under fairlygeneral 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 eigenvaluesof

T(t)with finite algebraic multiplicity, and the accumulation points ofsigma (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.

Files

Filename Size Approximate Download Time (Hours:Minutes:Seconds)

28.8 Modem 56K Modem ISDN (64 Kb) ISDN (128 Kb) Higher-speed Access dsong.pdf716.56 Kb 00:03:19 00:01:42 00:01:29 00:00:44 00:00:03

Browse All Available ETDs by
( Author |
Department )

If you have questions or technical problems, please Contact DLA.