标题： 线性时变微分代数方程的规范子空间及其在制定准确初始条件中的应用 显示英文标题

标题： Canonical Subspaces of Linear Time-Varying Differential-Algebraic Equations and Their Usefulness for Formulating Accurate Initial Conditions

摘要： 准确的初始条件的任务是精确地捕捉并固定所考虑流的自由积分常数。 这对于常规常微分方程来说是显而易见的，但对于微分代数方程（DAEs）则是一个复杂的问题，因为对于后者，这些自由常数隐藏在流中。 我们处理线性时变DAEs，并通过应用一种约简技术以及基于投影器的分析来获得准确的初始条件。 突出两个规范子空间起到了特殊的作用。 为了能够同时应用不同的DAE概念，我们首先证明了不同概念（消除未知数、约简、分解、奇异性和可解性）所基于的看似不同的秩条件实际上是一致的。 这使得能够独立于方法来理解正则性。 显示英文摘要

摘要： Accurate initial conditions have the task of precisely capturing and fixing the free integration constants of the flow considered. This is trivial for regular ordinary differential equations, but a complex problem for differential-algebraic equations (DAEs) because, for the latter, these free constants are hidden in the flow. We deal with linear time-varying DAEs and obtain an accurate initial condition by means of applying both a reduction technique and a projector based analysis. The highlighting of two canonical subspaces plays a special role. In order to be able to apply different DAE concepts simultaneously, we first show that the very different looking rank conditions on which the regularity notions of the different concepts (elimination of unknowns, reduction, dissection, strangeness, and tractability) are based are de facto consistent. This allows an understanding of regularity independent of the methods.