Stabilization of Kelvin-Voigt Damped Systems

1. Auflage 2022
ISBN: 978-3-031-12518-8
Verlag: Springer Nature Switzerland

Buch, Englisch, Band 47, 150 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 412 g

Reihe: Advances in Mechanics and Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Hassine, Fathi

Ammari, Kaïs

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Mathematik | Informatik Mathematik Mathematische Analysis
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik

Inhaltsverzeichnis

Preface.- Chapter 1. Preliminaries.- Chapter 2. Stability of elastic transmission systems with a local Kelvin-Voigt damping.- Chapter 3. Stabilization for the wave equation with singular Kelvin-Voigt damping.- Chapter 4. Logarithmic stabilization of the Euler-Bernoulli transmission plate equation with locally distributed Kelvin-Voigt damping.- Chapter 5. Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin-Voigt damping.- Chapter 6. Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping.- Chapter 7. Conclusion and perspectives.- Bibliography.