Name
Abstract | ||
|---|---|---|
We study existence of solutions, and in particular well-posedness, for a class of inhomogeneous, nonlinear partial differential equations (PDE’s). The main idea is to use system theory to write the nonlinear PDE as a well-posed infinite-dimensional linear system interconnected with a static nonlinearity. By a simple example, it is shown that in general well-posedness of the closed-loop system is not guaranteed. We show that well-posedness of the closed-loop system is guaranteed for linear systems whose input to output map is coercive for small times interconnected to monotone nonlinearities. This work generalizes the results presented in [1], where only globally Lipschitz continuous nonlinearities were considered. Furthermore, it is shown that a general class of linear port-Hamiltonian systems satisfies the conditions asked on the open-loop system. The result is applied to show well-posedness of a system consisting of a vibrating string with nonlinear damping at the boundary. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.sysconle.2019.04.002 | Systems & Control Letters |
Keywords | Field | DocType |
Well-posedness,Passive infinite-dimensional systems,Nonlinear feedback,Boundary feedback,port-Hamiltonian systems,Vibrating string,Nonlinear damping | Applied mathematics,Nonlinear system,Linear system,Control theory,Vibrating string,Lipschitz continuity,Partial differential equation,Mathematics,Monotone polygon | Journal |
Volume | ISSN | Citations |
128 | 0167-6911 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anthony Hastir | 1 | 0 | 0.68 |
| Federico Califano | 2 | 4 | 4.29 |
| Hans Zwart | 3 | 53 | 10.37 |