Overview
- 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)
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.
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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