Feedback theory extended for proving generation of contraction semigroups

Mikael Kurula*, Hans Zwart

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    1 Citation (Scopus)
    65 Downloads (Pure)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)617-647
    Number of pages31
    JournalJournal of evolution equations
    Volume16
    Issue number3
    DOIs
    Publication statusPublished - 1 Sep 2016

    Keywords

    • Contraction semigroup
    • Existence of solutions
    • Output feedback
    • Well-posed system

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