Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I write by Jérôme Le Rousseau. This book was released on 2022-03-28. Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I available in PDF, EPUB and Kindle. 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, Volume II
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II write by Jérôme Le Rousseau. This book was released on 2022-04-22. Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II available in PDF, EPUB and Kindle. 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
Elliptic Carleman Estimates and Applications to Stabilization and Controllability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Carleman Estimates and Applications to Stabilization and Controllability write by Jérôme Le Rousseau. This book was released on 2022. Elliptic Carleman Estimates and Applications to Stabilization and Controllability available in PDF, EPUB and Kindle. 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
Carleman Estimates for Second Order Partial Differential Operators and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Carleman Estimates for Second Order Partial Differential Operators and Applications write by Xiaoyu Fu. This book was released on 2019-10-31. Carleman Estimates for Second Order Partial Differential Operators and Applications available in PDF, EPUB and Kindle. 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 and Inverse Problems
Control and Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Control and Inverse Problems write by Kaïs Ammari. This book was released on 2023-09-26. Control and Inverse Problems available in PDF, EPUB and Kindle. 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.
