ON THE SPECTRUM OF THE TRANSPORT OPERATOR FOR A BOUNDED CONVEX BODY

The eigenvalue problem of the transport operator for a general bounded convex body V is studied mathematically. Where either V or the eigenfunction of the operator is not necessarily of spherical symmetry.It is shown that the spectrum of the operator consists of pure eigenvalues, possibly plusthe point of negative infinity.There is a countable infinity of real eigenvalues accumulating at minus infinity. Each eigenvalue, especially one in the left half-plane, is of index one, There is no complex (non-real) eigenvalue in the right half-plane Re λ>Σ. The solution of the corresponding initial-value problem is also discussed.     

NEUMANN SERIES SOLUTION FOR THE INTEGRAL BOLTZMANN TRANSPORT EQUATION

In this paper,a method based on Neumann series is proposed for solving stationary linear integral Boltzmann transport equations with variable energy for the case of both distributed and isotropic deltalike sources, by working in L~p(1≤p≤∞). The convergence of the Neumann series and convergent rate are established. In addition, a relation between stationary transport equation and time-dependent one is given.     

SOLUTION TO A PARAMETRIC EQUATION WITH GENERALIZED BOUNDARY CONDITION IN TRANSPORT THEORY

This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called δ-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue δ_0 is established.     

非均匀球对称介质中迁移算子的特征值的代数指标

动态迁移方程解的构造与迁移算子的谱分析紧密相关,特别是离散的特征值的分析,对应用尤为重要,但由于积—微分迁移算子是Banach空间中一无界的、且豫解算子不全连续的非对称算子,致使其谱分析的研究成为众所周知的困难课题,例如,对一类谱型,Jorgens类型的迁移算子的离散谱问题,Norton,Ukai,Lax和phiuips,阳     

一般非均匀凸介质的迁移算子本征值的代数指标

本文讨论一般非均匀凸介质所确定的迁移算子的本征值的代数指标问题.利用我们探索的线性算子法,完整地解决了一般非均匀凸介质中迁移问题的实本征值的代数指标问题,证明了迁移算子的每个实本征值的代数指标均为1.