线性微分代数方程边值问题：通过Kronecker标准形的可解性
Boundary value problems for linear differential-algebraic equations: solvability via the Kronecker canonical form
浏览论文内容
中文总结 AI 辅助
针对常系数微分代数方程两点边值问题，利用Kronecker标准形分解系统，结合参数化方法，给出奇异情形下解存在唯一性的判据与求解框架。
中文摘要 AI 辅助
研究了常系数微分代数方程的两点边值问题的可解性。与以往通常假设与方程相关的矩阵对是正则的研究不同，我们考虑了一般的奇异情形。利用Kronecker标准形，我们将问题分解为更简单的子系统，从而能够对可解性进行系统分析。参数化方法将边值问题约化为代数方程组。我们推导了解的存在性和唯一性的判据，并为求解此类边值问题提供了一个全面的框架。文中给出了几个说明性例子，展示了结果的应用性。
英文摘要
The solvability of two-point boundary value problems for constant-coefficient differential-algebraic equations is investigated. Unlike previous studies, which often assume that the matrix pair associated with the equation is regular, we consider the general singular case. Using the Kronecker canonical form, we decompose the problem into simpler subsystems, enabling a systematic analysis of solvability. The method of parameterization reduces the boundary value problem to a system of algebraic equations. We derive criteria for the existence and uniqueness of solutions and provide a comprehensive framework for solving such boundary value problems. Several illustrative examples are presented and show the applicability of the results.
发表机构
- Institute of Mathematics and Mathematical Modeling（数学与数学建模研究所）
- Institut für Mathematik, TU Ilmenau（图林根工业大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
