On Solvability of Dissipative Partial Differential-Algeraic Equations

被引：8

作者：

Jacob, Birgit ^{[1
,2
]}

Morris, Kirsten ^{[1
,2
]}

机构：

[1] Univ Wuppertal, Dept Math, D-42119 Wuppertal, Germany

[2] Univ Waterloo, Dept Appl Math KM, Waterloo, ON N2L 3G1, Canada

来源：

IEEE CONTROL SYSTEMS LETTERS | 2022年 / 6卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Differential-algebraic systems; distributed parameter systems; linear systems; stability of linear systems; DEGENERATE EVOLUTION-EQUATIONS; SEMIGROUP;

D O I：

10.1109/LCSYS.2022.3183479

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on reflexive Banach spaces is described. For dissipative partial differential equations the Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips generation theorem to dissipative differential-algebraic equations is given. The results are illustrated by coupled systems and the Dzektser equation.

引用

页码：3188 / 3193

页数：6

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