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

Title data

Mironchenko, Andrii:
Well-posedness and properties of the flow for semilinear evolution equations.
In: Mathematics of Control, Signals, and Systems. Vol. 36 (2024) Issue 3 . - pp. 483-523.
ISSN 0932-4194
DOI: https://doi.org/10.1007/s00498-023-00378-x

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Project information

Project title:
Project's official title
Project's id
Lyapunov theory meets boundary control systems
MI 1886/2-2

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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 C₀-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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: well-posedness; evolution equations; boundary control systems; infinite-dimensional systems; analytic systems
Subject classification: Mathematics Subject Classification Code: 93C25 37L05 47D06 (34H05 35K58 35K90 35Q93 37L15 93A15 93B52 93C10 93D05 93D09)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 06 Mar 2025 10:08
Last Modified: 06 Mar 2025 10:08
URI: https://eref.uni-bayreuth.de/id/eprint/92656