On higher index differential-algebraic equations in infinite dimensions

被引：6

作者：

Trostorff, Sascha ^{[1
]}

Waurick, Marcus ^{[2
]}

机构：

[1] Tech Univ Dresden, Fak Math, Inst Anal, Dresden, Germany

[2] Univ Strathclyde, Dept Math & Stat, Glasgow, Lanark, Scotland

来源：

DIVERSITY AND BEAUTY OF APPLIED OPERATOR THEORY | 2018年 / 268卷

关键词：

Differential-algebraic equations; higher index; infinite-dimensional state space; consistent initial values; distributional solutions;

D O I：

10.1007/978-3-319-75996-8_27

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for arbitrary initial values in a distributional sense. Moreover, we construct a nested sequence of subspaces for initial values in order to obtain classical solutions.

引用

页码：477 / 486

页数：10

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