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.
Carleman Estimates and Applications to Uniqueness and Control Theory
Carleman Estimates and Applications to Uniqueness and Control Theory - 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 and Applications to Uniqueness and Control Theory write by Feruccio Colombini. This book was released on 2012-12-06. Carleman Estimates and Applications to Uniqueness and Control Theory available in PDF, EPUB and Kindle. 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.
Carleman Estimates for the General Second Order Operators
Carleman Estimates for the General Second Order Operators - 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 the General Second Order Operators write by Nanhee Kim. This book was released on 2014-02. Carleman Estimates for the General Second Order Operators available in PDF, EPUB and Kindle. We derive Carleman estimates with two large parameters for a general partial differential operator of second order under explicit sufficient global conditions of pseudo-convexity on the weight function. We use these estimates to derive the most natural Carleman type estimates for the anisotropic system of elasticity with residual stress. Also, we give applications to uniqueness and stability of the continuation, observability, and identification of the residual stress from boundary measurements.
Carleman Inequalities
Carleman Inequalities - 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 Inequalities write by Nicolas Lerner. This book was released on 2019-05-18. Carleman Inequalities available in PDF, EPUB and Kindle. Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation. Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.
Control Of Partial Differential Equations
Control Of Partial Differential Equations - 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 Of Partial Differential Equations write by Jean-michel Coron. This book was released on 2023-04-11. Control Of Partial Differential Equations available in PDF, EPUB and Kindle. 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.
