Feedback theory extended for proving generation of contraction semigroups

A1 Journal article (refereed)

Internal Authors/Editors

Publication Details

List of Authors: Mikael Kurula, Hans Zwart
Publication year: 2016
Journal: Journal of Evolution Equations
Volume number: 16
Issue number: 3
Start page: 617
End page: 647
ISSN: 1424-3199
eISSN: 1424-3202


Recently, the following novel method for proving the existence of solutions for certain linear time-invariant PDEs was introduced: The operator associated with a given PDE is represented by a (larger) operator with an internal loop. If the larger operator (without the internal loop) generates a contraction semigroup, the internal loop is accretive, and some non-restrictive technical assumptions are fulfilled, then the original operator generates a contraction semigroup as well. Beginning with the undamped wave equation, this general idea can be applied to show that the heat equation and wave equations with damping are well-posed. In the present paper we show how this approach can benefit from feedback techniques and recent developments in well-posed systems theory, at the same time generalizing the previously known results. Among others, we show how well-posedness of degenerate parabolic equations can be proved.

Last updated on 2019-11-11 at 04:09