具有优化调整状态的供应链系统算子的性质

Properties of the System Operator for the Supply Chain System with State of Optimal Adjustment

摘要: 研究了一类具有优化调整状态的供应链系统。通过选取空间和定义算子将模型方程转化成抽象柯西问题，运用C₀半群理论，证明了系统算子是稠密的预解正算子，得出了系统算子的共轭算子及其定义域，并证明了系统算子的增长界为0。最后运用预解正算子中共尾的概念及相关理论证明了系统算子的谱上界也是0。

Abstract: The paper presents a supply chain system with state of optimal adjustment. By choosing space and defining operator of this system, we transfer this model into an abstract Cauchy problem. Using C₀ semigroup theory, we first prove the system operator is a densely defined resolvent positive op-erator. We obtain the adjoint operator of the system operator and its domain. Furthermore, we prove that 0 is the growth bound of the system operator. Finally, we show that 0 is also the upper spectral bound of the system operator using the concept of cofinal and relative theory.