On higher index differential-algebraic equations in infinite dimensions

被引：7

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

共 8 条

[1] The quasi-Weierstrass form for regular matrix pencils [J].

Berger, Thomas ;

Ilchmann, Achim ;

Trenn, Stephan .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (10) :4052-4069

[2]

DAI L, 1989, LECT NOTES CONTR INF, V118, P1

[3] A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term [J].

Kalauch, Anke ;

Picard, Rainer ;

Siegmund, Stefan ;

Trostorff, Sascha ;

Waurick, Marcus .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2014, 26 (02) :369-399

[4]

Kunkel P., 2006, Differential-Algebraic Equations. Analysis and Numerical Solution

[5]

Picard R., 1989, PITMAN RES NOTES MAT, V196

[6] A structural observation for linear material laws in classical mathematical physics [J].

Picard, Rainer .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2009, 32 (14) :1768-1803

[7]

Rudin W., 1987, Real and Complex Analysis, V3

[8]

Trostor S., 2017, EFFERENTIAL ALGEBRAI

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