Well-posedness and properties of the flow for semilinear evolution equations
Optimization and Control
2023-11-13 v3 Analysis of PDEs
Dynamical Systems
Functional Analysis
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 -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.
Keywords
Cite
@article{arxiv.2211.00433,
title = {Well-posedness and properties of the flow for semilinear evolution equations},
author = {Andrii Mironchenko},
journal= {arXiv preprint arXiv:2211.00433},
year = {2023}
}