运输网络模型在Hilbert空间中的解展开

EXPANSION OF SOLUTION OF TRANSPORT NETWORK IN HILBERT SPACE

针对一个具体的实际问题-双向边的三角形运输网路模型,研究系统动态解的结构.首先,对这一类交通运输网络模型的系统算子进行谱分析,给出系统算子本征值和本征向量的表达式.其次,指出尽管其系统算子的本征向量在状态空间中不完整,但当时间t大于某一时刻时,系统解仍可按照其本征向量完全展开.

In this paper, we study a practical problem-A regular triangle bi-directed transport network, mainly considering its solution structure. First, we give spectral analysis for the transport network and obtain the expression for system eigenvalues and eigenvectors. Then, we show that even if the eigenvectors are incomplete in state space, the system solution can expand according with eigenvectors without remainder term when t is larger than a certain constant.