Well-posedness and properties of the flow for semilinear evolution equations

被引：0

作者：

Mironchenko, Andrii ^{[1
]}

机构：

[1] Univ Passau, Fac Comp Sci & Math, Passau, Germany

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2024年 / 36卷 / 03期

关键词：

Well-posedness; Evolution equations; Boundary control systems; Infinite-dimensional systems; Analytic systems; TO-STATE STABILITY; SMALL-GAIN THEOREM; BOUNDARY DISTURBANCES; FEEDBACK-SYSTEMS; INFINITE; ISS; STABILIZATION; RESPECT;

D O I：

10.1007/s00498-023-00378-x

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 derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity, bounded-implies-continuation property, boundedness of reachability sets, etc. These properties represent a basic toolbox for stability and robustness analysis of semilinear boundary control systems. We cover systems governed by general C-0-semigroups, and analytic semigroups that may have both boundary and distributed disturbances. We illustrate our findings on an example of a Burgers' equation with nonlinear local dynamics and both distributed and boundary disturbances.

引用

页码：483 / 523

页数：41

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