On the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditions

dc.contributor.authorSong, Degongen
dc.contributor.committeechairGreenberg, Williamen
dc.contributor.committeememberHaskell, Peter E.en
dc.contributor.committeememberKohler, Werner E.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberHagedorn, George A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:08:02Zen
dc.date.adate2000-03-17en
dc.date.available2014-03-14T20:08:02Zen
dc.date.issued2000-02-14en
dc.date.rdate2001-03-17en
dc.date.sdate2000-03-07en
dc.description.abstractThis 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 <I>L^p</I> including <I>L^1</I>. Some aspects of the spectral properties of the transport operator <I>A</I> and the strongly continuous semigroup <I>T(t)</I> generated by <I>A</I> 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 <I>T(t)</I> outside the disk {lambda : |lambda| leq exp (-lambda^{ast} t)} consists of isolated eigenvalues of <I>T(t)</I> 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-03072000-23200015en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03072000-23200015/en
dc.identifier.urihttp://hdl.handle.net/10919/26375en
dc.publisherVirginia Techen
dc.relation.haspartdsong.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjecttransport equationen
dc.subjectspectrumen
dc.subjectstabilityen
dc.subjectstrongly continuous semigroupen
dc.titleOn the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditionsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en
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