Feedback theory extended for proving generation of contraction semigroups

Mikael Kurula, Hans Zwart

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
44 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

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Contraction Semigroup
Operator
Internal
Wave equation
Degenerate Parabolic Equation
Systems Theory
Well-posedness
Heat Equation
Linear Time
Existence of Solutions
Damping
Invariant

Keywords

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

Cite this

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Feedback theory extended for proving generation of contraction semigroups. / Kurula, Mikael; Zwart, Hans.

In: Journal of evolution equations, Vol. 16, No. 3, 01.09.2016, p. 617-647.

Research output: Contribution to journalArticleAcademicpeer-review

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