Feedback theory extended for proving generation of contraction semigroups

Mikael Kurula, Hans Zwart

    Research output: Book/ReportCommissioned reportProfessional

    Abstract

    Recently, the following novel method for proving the existence of solutions for certain linear time-invariant PDEs was introduced: The operator associated to 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 generalising the previously known results. Among others, we show how well-posedness of degenerate parabolic equations can be proved.
    Original languageUndefined/Unknown
    PublisherCornell University Library, arXiv.org
    Publication statusPublished - 2014
    MoE publication typeD4 Published development or research report or study

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