缓发中子迁移方程的适定性及相应迁移算子的谱分布

The Well-posed and the Spectral PropertieS of the Transport Equation with Delayed Neutrons

本文在Ｈｉｌｂｅｒｔ空间Ｈ中讨论了带广义边界条件、单迷、散射和裂变是各向同性，具ｎ（ｎ≥１）个缓发中子群的中子迁移方程。运用正线性算子及其Ｃ。—半群理论，首先证明了此方程非负解的存在唯一性；其次讨论了带方程所确定的迁移算子的谱分布，证明了其剩余谱为空集，右半平面除了至多可数个离散本征值与ｎ个连续谱点外属于它的预解集。最后证明了迁移算子占优本征值的存在性。

This paper discusses the monoenergetic neutron transsport equation in slab,isotropic scattion and fisslon with generalized boundary conditions and deleyed neutrons inHilbert space H。First,the wellposed prlblcm is proved by means of the theory of positive op-erators and Co-semigraup.Second,the spectral properties of the transport operator A is dis-cussed:the residual spectrum of A is a vacuous set,the right half plane deleting the pointspectrum and continuous spectrum{-λ_i|i=1,2,…,n}of A belongs to the resolventset.Fi-nally,it is proved that the transpert operator A has a dominant eigenvalue β。