In this paper, we consider linear boundary port-Hamiltonian distributed parameter systems on a time-varying spatial domain. We derive the specific time-varying Dirac structure that these systems give rise to and use it to formally introduce a new class of moving-boundary port-Hamiltonian systems by showing that these distributed parameter systems on a time-varying spatial domain admit a port-Hamiltonian representation. We demonstrate that our results can be leveraged to develop a spatial discretization scheme with dynamic meshing for approximating the telegrapher's equations on a time-varying spatial domain, which we subsequently verify numerically.

翻译：本文研究了时变空间域上的线性边界端口哈密顿分布参数系统。我们推导了这类系统所对应的特定时变狄拉克结构，并通过证明时变空间域上的分布参数系统具有端口哈密顿表示形式，正式引入了一类新的移动边界端口哈密顿系统。我们证明了该结果可用于开发具有动态网格的空间离散化方案，以近似时变空间域上的电报方程，并通过数值计算验证了该方法的有效性。