论文标题
关于无限网络中流量的渐近行为
On the asymptotic behaviour of semigroups for flows in infinite networks
论文作者
论文摘要
我们研究无限网络上的运输过程。这些过程的解决方案可以由操作员半群在合适的Banach空间上建模。从经典上讲，这样的半群是很连续的，因此它们的渐近行为被充分理解。但是，最近出现了新的运输过程示例，而相应的半群并不是很连续的。由于缺乏强大的连续性，目前对这些半群的长期行为的结果很少。在本文中，我们讨论了这些运输过程的某些类别的渐近行为。特别是，事实证明，解决方案半群在操作员规范上表现出渐近的周期性，这是由于含有乘法运算符的正长期行为对长期行为产生了更一般的结果。此外，我们对无限网络上运输过程的渐近行为进行了已知的结果，并证明其扩展的渐近周期性对有限度量的空间。
We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic behaviour is quite well understood. However, recently new examples of transport processes emerged where the corresponding semigroup is not strongly continuous. Due to this lack of strong continuity, there are currently only few results on the long-term behaviour of these semigroups. In this paper, we discuss the asymptotic behaviour for a certain class of these transport processes. In particular, it is proved that the solution semigroups behave asymptotically periodic with respect to the operator norm as a consequence of a more general result on the long-term behaviour by positive semigroups containing a multiplication operator. Furthermore, we revisit known results on the asymptotic behaviour of transport processes on infinite networks and prove the asymptotic periodicity of their extensions to the space of bounded measures.
