抽象耗散哈密顿微分代数方程无处不在
Abstract dissipative Hamiltonian differential-algebraic equations are everywhere
AI总结：
该研究提出可将含物理约束及多种标准偏微分方程模型转化为扩展状态空间上的耗散哈密顿结构抽象微分代数方程，并用统一算子理论方法分析其性质、给出应用实例。
摘要：
本文研究将偏微分方程（PDE）表示为具有耗散哈密顿结构的抽象微分代数方程（adHDAE）的方法。我们证明，这类系统不仅在底层物理存在约束时会出现，许多标准PDE模型都可被视为扩展状态空间上的adHDAE，这反映了模型通常包含闭合关系与结构特性的事实。我们提出了一种统一的算子理论方法来分析这类算子方程的性质，并通过若干应用实例进行了说明。
英文摘要：
In this paper we study the representation of partial differential equations (PDEs) as abstract differential-algebraic equations (DAEs) with dissipative Hamiltonian structure (adHDAEs). We show that these systems not only arise when there are constraints coming from the underlying physics, but many standard PDE models can be seen as an adHDAE on an extended state space. This reflects the fact that models often include closure relations and structural properties. We present a unifying operator theoretic approach to analyze the properties of such operator equations and illustrate this by several applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
