@article{Mironchenko2023, author = {Mironchenko, Andrii}, title = {Well-posedness and properties of the flow for semilinear evolution equations}, series = {Mathematics of Control, Signals, and Systems}, volume = {36}, journal = {Mathematics of Control, Signals, and Systems}, number = {3}, publisher = {Springer Nature}, address = {Berlin}, doi = {10.1007/s00498-023-00378-x}, url = {http://nbn-resolving.de/urn:nbn:de:101:1-2024022307494197431619}, pages = {483 -- 523}, year = {2023}, abstract = {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.}, language = {en} }