Elliptic Carleman Estimates And Applications To Stabilization And Controllability Volume Ii

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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II

Author : Jérôme Le Rousseau
Publisher : Springer Nature
ISBN 13 : 3030886700
Total Pages : 542 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II by : Jérôme Le Rousseau

Download or read book Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II written by Jérôme Le Rousseau and published by Springer Nature. This book was released on 2022-04-22 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation. Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions. The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds. Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates. The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I

Author : Jérôme Le Rousseau
Publisher : Springer Nature
ISBN 13 : 3030886743
Total Pages : 410 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I by : Jérôme Le Rousseau

Download or read book Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I written by Jérôme Le Rousseau and published by Springer Nature. This book was released on 2022-03-28 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.

Elliptic Carleman Estimates and Applications to Stabilization and Controllability

Author : Jérôme Le Rousseau
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)

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Book Synopsis Elliptic Carleman Estimates and Applications to Stabilization and Controllability by : Jérôme Le Rousseau

Download or read book Elliptic Carleman Estimates and Applications to Stabilization and Controllability written by Jérôme Le Rousseau and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.

Carleman Estimates for Second Order Partial Differential Operators and Applications

Author : Xiaoyu Fu
Publisher : Springer Nature
ISBN 13 : 3030295303
Total Pages : 127 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Carleman Estimates for Second Order Partial Differential Operators and Applications by : Xiaoyu Fu

Download or read book Carleman Estimates for Second Order Partial Differential Operators and Applications written by Xiaoyu Fu and published by Springer Nature. This book was released on 2019-10-31 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.

Control Of Partial Differential Equations

Author : Jean-michel Coron
Publisher : World Scientific
ISBN 13 : 981127164X
Total Pages : 315 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Control Of Partial Differential Equations by : Jean-michel Coron

Download or read book Control Of Partial Differential Equations written by Jean-michel Coron and published by World Scientific. This book was released on 2023-04-11 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.

Control and Inverse Problems

Author : Kaïs Ammari
Publisher : Springer Nature
ISBN 13 : 3031356756
Total Pages : 276 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Control and Inverse Problems by : Kaïs Ammari

Download or read book Control and Inverse Problems written by Kaïs Ammari and published by Springer Nature. This book was released on 2023-09-26 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 systems Information transfer in multiplier equations Nonparametric instrumental regression Control of chained systems The 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.

Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations

Author : Genni Fragnelli
Publisher : American Mathematical Soc.
ISBN 13 : 1470419548
Total Pages : 83 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations by : Genni Fragnelli

Download or read book Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations written by Genni Fragnelli and published by American Mathematical Soc.. This book was released on 2016-06-21 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.

Controllability and Stabilization of Parabolic Equations

Author : Viorel Barbu
Publisher : Springer
ISBN 13 : 331976666X
Total Pages : 226 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Controllability and Stabilization of Parabolic Equations by : Viorel Barbu

Download or read book Controllability and Stabilization of Parabolic Equations written by Viorel Barbu and published by Springer. This book was released on 2018-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear differential equations, Controllability and Stabilization of Parabolic Equations is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.

Identification and Control: Some New Challenges

Author : Kaïs Ammari
Publisher : American Mathematical Soc.
ISBN 13 : 1470455471
Total Pages : 185 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Identification and Control: Some New Challenges by : Kaïs Ammari

Download or read book Identification and Control: Some New Challenges written by Kaïs Ammari and published by American Mathematical Soc.. This book was released on 2020-11-12 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Summer School on Identification and Control: some challenges, held from June 18–20, 2019, in Monastir, Tunisia. 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.

Carleman Estimates and Applications to Uniqueness and Control Theory

Author : Feruccio Colombini
Publisher : Springer Science & Business Media
ISBN 13 : 1461202035
Total Pages : 217 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Carleman Estimates and Applications to Uniqueness and Control Theory by : Feruccio Colombini

Download or read book Carleman Estimates and Applications to Uniqueness and Control Theory written by Feruccio Colombini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza tion, observability and exact control for the wave and the SchrOdinger equations. A final paper presents a challenging list of open problems on the topic of control lability of linear and sernilinear heat equations. The papers contain exhaustive and essentially self-contained proofs directly ac cessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors are L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E. Zuazua.

Stabilization of Kelvin-Voigt Damped Systems

Author : Kaïs Ammari
Publisher : Springer Nature
ISBN 13 : 3031125193
Total Pages : 156 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Stabilization of Kelvin-Voigt Damped Systems by : Kaïs Ammari

Download or read book Stabilization of Kelvin-Voigt Damped Systems written by Kaïs Ammari and published by Springer Nature. This book was released on 2022-09-20 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Global Carleman Estimates for Degenerate Parabolic Operators with Applications

Author : P. Cannarsa
Publisher : American Mathematical Soc.
ISBN 13 : 1470414961
Total Pages : 209 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Global Carleman Estimates for Degenerate Parabolic Operators with Applications by : P. Cannarsa

Download or read book Global Carleman Estimates for Degenerate Parabolic Operators with Applications written by P. Cannarsa and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.

Fluids Under Control

Author : Tomáš Bodnár
Publisher : Springer Nature
ISBN 13 : 3031473558
Total Pages : 376 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Fluids Under Control by : Tomáš Bodnár

Download or read book Fluids Under Control written by Tomáš Bodnár and published by Springer Nature. This book was released on with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inverse Problems for Partial Differential Equations

Author : Victor Isakov
Publisher : Springer
ISBN 13 : 3319516582
Total Pages : 406 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Inverse Problems for Partial Differential Equations by : Victor Isakov

Download or read book Inverse Problems for Partial Differential Equations written by Victor Isakov and published by Springer. This book was released on 2017-02-24 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.

Probabilistic Methods in Geometry, Topology and Spectral Theory

Author : Yaiza Canzani
Publisher : American Mathematical Soc.
ISBN 13 : 1470441454
Total Pages : 197 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Probabilistic Methods in Geometry, Topology and Spectral Theory by : Yaiza Canzani

Download or read book Probabilistic Methods in Geometry, Topology and Spectral Theory written by Yaiza Canzani and published by American Mathematical Soc.. This book was released on 2019-11-20 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22–26, 2016 and Probabilistic Methods in Topology, held from November 14–18, 2016 at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. Probabilistic methods have played an increasingly important role in many areas of mathematics, from the study of random groups and random simplicial complexes in topology, to the theory of random Schrödinger operators in mathematical physics. The workshop on Probabilistic Methods in Spectral Geometry and PDE brought together some of the leading researchers in quantum chaos, semi-classical theory, ergodic theory and dynamical systems, partial differential equations, probability, random matrix theory, mathematical physics, conformal field theory, and random graph theory. Its emphasis was on the use of ideas and methods from probability in different areas, such as quantum chaos (study of spectra and eigenstates of chaotic systems at high energy); geometry of random metrics and related problems in quantum gravity; solutions of partial differential equations with random initial conditions. The workshop Probabilistic Methods in Topology brought together researchers working on random simplicial complexes and geometry of spaces of triangulations (with connections to manifold learning); topological statistics, and geometric probability; theory of random groups and their properties; random knots; and other problems. This volume covers recent developments in several active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.

Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems

Author : Mourad Bellassoued
Publisher : Springer
ISBN 13 : 4431566007
Total Pages : 260 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems by : Mourad Bellassoued

Download or read book Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems written by Mourad Bellassoued and published by Springer. This book was released on 2017-11-23 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of which has been established within a very general framework, so that the method using Carleman estimates for inverse problems is misunderstood as being very difficult. The main purpose of the book is to provide an accessible approach to the methodology. To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. Thus a direct and concrete means was chosen not only because it is friendly to readers but also is much more relevant. By practical necessity, there is surely a wide range of inverse problems and the method delineated here can solve them. The intention is for readers to learn that method and then apply it to solving new inverse problems.

Inverse Problems and Carleman Estimates

Author : Michael V. Klibanov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110745550
Total Pages : 247 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Inverse Problems and Carleman Estimates by : Michael V. Klibanov

Download or read book Inverse Problems and Carleman Estimates written by Michael V. Klibanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-09-07 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.