具有积分边界条件板对称中子迁移方程的适定性

Wellposed Problem for the Neutron Transport Equation in a Slab with Integral Boundary Condition

本文讨论一类具积分边界条件的板对称中子迁移方程的适定性,首先,我们证明了该方程正解的存在唯一性,其次,我们证明了相应的迁移算子的占优本征值的存在性并指出了当t→+∞时迁移方程解的渐近行为。

In this paper, the neutron transport equation in a slab with integral boundary conditions and initial values is considered. First,the existence and uniqueness of positive solution of the equation are proved. Second, the existence of the dominant eigenvalue for corresponding neutron transport operator and the asymptotic behavior of the solution as t→+∞ are discussed.