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On Polynomial Stability of Coupled Partial Differential Equations in 1D

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Semigroups of Operators – Theory and Applications (SOTA 2018)

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Abstract

We study the well-posedness and asymptotic behaviour of selected PDE–PDE and PDE–ODE systems on one-dimensional spatial domains, namely a boundary coupled wave–heat system and a wave equation with a dynamic boundary condition. We prove well-posedness of the models and derive rational decay rates for the energy using an approach where the coupled systems are formulated as feedback interconnections of impedance passive regular linear systems.

The research is supported by the Academy of Finland Grant numbers 298182 and 310489 held by L. Paunonen.

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Authors and Affiliations

  1. Mathematics and Statistics, Faculty of Information Technology and Communication Sciences, Tampere University, P.O. Box 692, 33101, Tampere, Finland

    Lassi Paunonen

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  1. Lassi Paunonen
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Correspondence to Lassi Paunonen .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield, South Africa

    Jacek Banasiak

  2. Department of Mathematics, Lublin University of Technology, Lublin, Poland

    Adam Bobrowski

  3. Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw, Poland

    Mirosław Lachowicz

  4. Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

    Yuri Tomilov

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Paunonen, L. (2020). On Polynomial Stability of Coupled Partial Differential Equations in 1D. In: Banasiak, J., Bobrowski, A., Lachowicz, M., Tomilov, Y. (eds) Semigroups of Operators – Theory and Applications. SOTA 2018. Springer Proceedings in Mathematics & Statistics, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-030-46079-2_20

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