Stabilization of Kelvin-Voigt Damped Systems

Kaïs Ammari, Fathi Hassine

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English

Birkhauser Verlag AG
21 September 2022

Cybernetics & systems theory; Calculus & mathematical analysis; Mechanics of solids

Series: 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.

By: Kaïs Ammari, Fathi Hassine
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: 2022 ed.
Volume: 47
Dimensions: Height: 235mm, Width: 155mm,
Weight: 412g
ISBN: 9783031125188
ISBN 10: 3031125185
Series: Advances in Mechanics and Mathematics
Pages: 150
Publication Date: 21 September 2022
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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.

Reviews for Stabilization of Kelvin-Voigt Damped Systems

“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)