Differential-Algebraic Equations from a Functional-Analytic Viewpoint: A Survey
Differential-Algebraic Equations from a Functional-Analytic Viewpoint: A Survey
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从泛函分析的角度看微分代数方程：一项调查
DOI：
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发表时间：
2015
期刊：
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通讯作者：
R. März
中科院分区：
文献类型：
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作者：
R. März
本文的目的是提供一个概述的艺术状态有关的功能分析性质与微分代数方程（DAE）。我们总结了相关文献，发展了线性和非线性微分代数算子的基本理论。特别是，我们考虑Fredholm性质，正常的可解性，广义逆，最小二乘解，分裂的定期线性微分代数算子，有界的外部逆，局部可解性的方程与定期非线性微分代数算子，牛顿-Kantorovich迭代，和正则化的不适定问题所产生的高指标运营商。
The purpose of this paper is to provide an overview on the state of the art concerning functional-analytic properties associated with differential-algebraic equations (DAEs). We summarize the relevant literature and develop a basic theory of linear and nonlinear differential-algebraic operators. In particular, we consider Fredholm properties, normal solvability, generalized inverses, least-squares solutions, splittings of regular linear differential-algebraic operators, bounded outer inverses, local solvability of equations with regular nonlinear differential-algebraic operators, Newton–Kantorovich iterations, and regularizations of the ill-posed problems arising from higher-index operators.