Stabilization of Kelvin-Voigt Damped Systems
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Beschreibung
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.
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.
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
Autor*in
Kaïs Ammari
Themen in »Stabilization of Kelvin-Voigt Damped Systems«
Kelvin Voigt PDEs Kelvin Voigt damping Kelvin-Voigt control theory Kelvin Voigt stability Stabilization elastic systems Elastic transmission systems Logarithmic stabilization Semigroups bounded linear operators Euler Bernoulli transmission Energy decay damped Asymptotic behavior Euler Bernoulli
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“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)
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