Kaïs Ammari - Böcker

The articles cover new developments in control theory and inverse problems. First, the problem of Calderón, which consists of determining a conductivity appearing in an elliptic equation from excitation and measurements on a part of the boundary of the domain, is studied. Second, an introduction to the mathematical analysis of inverse spectral problems of Borg- Levinson type is presented. Third, the control of multi-component systems of wave equations, focusing on the notion of simultaneous control (using the same control scheme in all components of the system at hand) and indirect control (using a single control for a system consisting of two components), is presented. Last, the study of the cost of control for parabolic systems, the finite time stabilization of hyperbolic control systems by boundary feedback laws, and image reconstruction by data assimilation are addressed.

The structures considered consist of finitely interconnected flexible elements such as strings and beams (or combinations thereof), distributed along a planar network.

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.

This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields” held at the University of Sidi Bel Abbès, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as:Sobolev spaces and elliptic boundary value problemsLocal energy solutions of the nonlinear wave equationGeometric control of eigenfunctions of Schrödinger operatorsResearch in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.

This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields” held at the University of Sidi Bel Abbès, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as:Sobolev spaces and elliptic boundary value problemsLocal energy solutions of the nonlinear wave equationGeometric control of eigenfunctions of Schrödinger operatorsResearch in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.

This brief provides unified methods for the stabilization of some fractional evolution systems, nicely complementing existing literature on fractional calculus.

This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control & Inverse Problems” held in Monastir, Tunisia in May 2022. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as:Controllability of dynamical systemsInformation transfer in multiplier equationsNonparametric instrumental regressionControl of chained systemsThe damped wave equation Control and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.

This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control & Inverse Problems” held in Monastir, Tunisia in May 2022. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as:Controllability of dynamical systemsInformation transfer in multiplier equationsNonparametric instrumental regressionControl of chained systemsThe damped wave equation Control and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.

This volume presents a timely overview of control theory and related topics, such as the reconstruction problem, the stability of PDEs, and the Calderón problem.

This volume presents a timely overview of control theory and related topics, such as the reconstruction problem, the stability of PDEs, and the Calderón problem. The chapters are based on talks given at the conference "Control & Related Fields” held in Seville, Spain in March 2023. In addition to providing a snapshot of these areas, chapters also highlight breakthroughs on more specific topics, such as:Stabilization of an acoustic systemThe Kramers-Fokker-Planck operatorControl of parabolic equationsControl of the wave equationAdvances in Partial Differential Equations and Control will be a valuable resource for both established researchers as well as more junior members of the community.

This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas.

This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control Theory & Inverse Problems” held in Monastir, Tunisia in May 2023. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as:Control of hyperbolic systemsThe Helffer-Nier ConjectureRapid stabilization of the discretized Vlasov systemExponential stability of a delayed thermoelastic systemControl Theory and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.

This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control Theory & Inverse Problems” held in Monastir, Tunisia in May 2024. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as:Neural network modelingOptimal control of the Euler-Bernoulli equationTraffic signal controlSpectral description of a cell growth and division equationControl Theory and Inverse Problems will be a valuable resource for both established researchers as well as more junior members of the community.