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Stabilization of Kelvin-Voigt Damped Systems

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  • © 2022

Overview

Authors:
  1. Kaïs Ammari

    1. Department of Mathematics, University of Monastir, Monastir, Tunisia

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  2. Fathi Hassine

    1. Department of Mathematics, University of Monastir, Monastir, Tunisia

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  • Examines the stability of a variety of coupled systems with local Kelvin-Voigt damping
  • Reviews the development in the stability analysis of elastic structures with local Kelvin-Voigt damping
  • Serves as a timely resource for researchers studying control theory of PDEs

Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 47)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Preliminaries

    • Kaïs Ammari, Fathi Hassine
    Pages 1-8

  3. Stability of Elastic Transmission Systems with a Local Kelvin–Voigt Damping

    • Kaïs Ammari, Fathi Hassine
    Pages 9-37

  4. Stabilization for the Wave Equation with Singular Kelvin–Voigt Damping

    • Kaïs Ammari, Fathi Hassine
    Pages 39-63

  5. Logarithmic Stabilization of the Euler–Bernoulli Transmission Plate Equation with Locally Distributed Kelvin–Voigt Damping

    • Kaïs Ammari, Fathi Hassine
    Pages 65-84

  6. Energy Decay Estimates of Elastic Transmission Wave/Beam Systems with a Local Kelvin–Voigt Damping

    • Kaïs Ammari, Fathi Hassine
    Pages 85-119

  7. Asymptotic Behavior of the Transmission Euler–Bernoulli Plate and Wave Equation with a Localized Kelvin–Voigt Damping

    • Kaïs Ammari, Fathi Hassine
    Pages 121-142

  8. Conclusion and Perspectives

    • Kaïs Ammari, Fathi Hassine
    Pages 143-145

  9. Back Matter

    Pages 147-150
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Keywords

About this book

This monograph examines the stability of various coupled systems with local Kelvin-Voigt damping. The development of this area is thoroughly reviewed along with the authors’ contributions. New results are featured on the fundamental properties of solutions of linear transmission evolution PDEs involving Kelvin-Voigt damping, with special emphasis on the asymptotic behavior of these solutions. The vibrations of transmission problems are highlighted as well, making this a valuable resource for those studying this active area of research. 

The book begins with a brief description of the abstract theory of linear evolution equations with a particular focus on semigroup theory. Different types of stability are also introduced along with their connection to resolvent estimates. After this foundation is established, different models are presented for uni-dimensional and multi-dimensional linear transmission evolution partial differential equations with Kelvin-Voigt damping.Stabilization of Kelvin-Voigt Damped Systems will be a useful reference for researchers in mechanics, particularly those interested in the study of control theory of PDEs.

Reviews

“The monograph describes the physical meaning of the problems under consideration, which confirms their relevance and undoubtedly arouses interest among people involved in applied research. For each problem, the results presented are given with references on used methods and ideas, as well as for previously known results. This makes it possible to get a more complete picture of the development of the theory of stability of systems with Kelvin-Voigt damping.” (Mikhail Turbin, zbMATH 1512.35001, 2023)

Authors and Affiliations

  • Department of Mathematics, University of Monastir, Monastir, Tunisia

    Kaïs Ammari, Fathi Hassine

Bibliographic Information

  • Book Title: Stabilization of Kelvin-Voigt Damped Systems

  • Authors: Kaïs Ammari, Fathi Hassine

  • Series Title: Advances in Mechanics and Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-12519-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-12518-8Published: 21 September 2022

  • Softcover ISBN: 978-3-031-12521-8Published: 22 September 2023

  • eBook ISBN: 978-3-031-12519-5Published: 20 September 2022

  • Series ISSN: 1571-8689

  • Series E-ISSN: 1876-9896

  • Edition Number: 1

  • Number of Pages: X, 150

  • Number of Illustrations: 6 illustrations in colour

  • Topics: Analysis, Systems Theory, Control, Solid Mechanics

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