Song, Degong2014-03-142014-03-142000-02-14etd-03072000-23200015http://hdl.handle.net/10919/26375This 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.In Copyrighttransport equationspectrumstabilitystrongly continuous semigroupDissertationhttp://scholar.lib.vt.edu/theses/available/etd-03072000-23200015/