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.
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页码：3188 / 3193
页数：6
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