缓发中子迁移方程的谱逼近理论

Spectral Approximation Theory for Transport Equation with Delayed Neutrons

本文运用Ｐ一阶拟总体列紧算子逼近理论，对介质占据三维欧氏空间中一有界凸体，散射和裂变是各向导性的具Ｎ个缓发中子群的单能非定态迁移方程。证明了：（１）、具缓发中子迁移算子的占优未征值可由相应的离散纵标迁移算了所确定的具非负未征函数且实部为最大的未征值逼近；（２）。

The time dependent neutron transport system in bounded convex media inthree一dimensionaI Euclidean space with anistropic scatting and fission and delayed neutronsis considered.By mean of the approximation theory of p一order quasi一collectively compactoperators,the following results are proved :(Ⅰ)The dominant eigenvalue of the transportoperator with delayed neutron can be approximated by the eigenvalue associated with thetransport operator of corresponding discrete一ordinate. which is the largest(in the real part)of all the other eigenvalue and has at least one nonnegative eigenfunction,(Ⅱ)The positiveeigenfunction of the dominant eigenvalue can be approximated by the nonnegative eigenfunc-tion associated with the eigenvalue of discrete ordinate transport operator with the largest(inthe real part)of all the other eigenvalue