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

Related URLs

Project information

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.