at Google ScholarTitle 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
| Review: |
Related URLs
Project information
| Project title: |
Project's official title Project's id Lyapunov theory meets boundary control systems MI 1886/2-2 |
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| 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 |