电报系统的网络和港口汉密尔顿。Ⅲ。显性表征和长期行为

J. Banasiak, Adam Bloch
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摘要

本文给出了度量图上满足一般线性Kirchhoff型边界条件的双曲型系统解的半群的显式公式。此外,我们使用这种表示来建立解决方案的长期行为。边界矩阵的谱分解起着至关重要的作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour
In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.
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