Download or read book Carleman Estimates for the General Second Order Operators written by Nanhee Kim and published by LAP Lambert Academic Publishing. This book was released on 2014-02 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Carleman Estimates for the General Second Order Operators and Applications to Inverse Problems written by Nanhee Kim and published by . This book was released on 2010 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive Carleman estimates with two large parameters for a general partial di erential operator of second order under explicit su cient 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 identi cation of the residual stress from boundary measurements.
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.
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.
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.
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.
Download or read book Carleman Inequalities written by Nicolas Lerner and published by Springer. This book was released on 2019-05-18 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Carleman Estimates for Coefficient Inverse Problems and Numerical Applications written by Michael V. Klibanov and published by Walter de Gruyter. This book was released on 2012-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the main subject of the author's considerations is coefficient inverse problems. Arising in many areas of natural sciences and technology, such problems consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals. Although the authors pay strong attention to the rigorous justification of known results, they place the primary emphasis on new concepts and developments.
Download or read book Inverse Problems and Related Topics written by Jin Cheng and published by Springer Nature. This book was released on 2020-02-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 13 chapters, which are extended versions of the presentations at International Conference on Inverse Problems at Fudan University, Shanghai, China, October 12-14, 2018, in honor of Masahiro Yamamoto on the occasion of his 60th anniversary. The chapters are authored by world-renowned researchers and rising young talents, and are updated accounts of various aspects of the researches on inverse problems. The volume covers theories of inverse problems for partial differential equations, regularization methods, and related topics from control theory. This book addresses a wide audience of researchers and young post-docs and graduate students who are interested in mathematical sciences as well as mathematics.
Download or read book Expansions in Eigenfunctions of Selfadjoint Operators written by I͡Uriĭ Makarovich Berezanskiĭ and published by American Mathematical Soc.. This book was released on 1968 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Geometric Methods in the Control of Partial Differential Equations written by Robert Gulliver and published by American Mathematical Soc.. This book was released on 2000 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on "Differential Geometric Methods in the Control of Partial Differential Equations", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic. Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume - written by specialists in PDEs and control of PDEs as well as by geometers - collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects-differential geometry and control of PDEs-have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.
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 225 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.
Download or read book Sobolev Spaces in Mathematics III written by Victor Isakov and published by Springer Science & Business Media. This book was released on 2008-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, marking the centenary of S.L. Sobolev’s birth, presents the latest the results on some important problems of mathematical physics. The book contains two short biographical articles and unique archive photos of S. Sobolev.
Download or read book partial differential equation methods in control and shape analysis written by Giuseppe Da Prato and published by CRC Press. This book was released on 1997-02-20 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the International Federatiojn for Information Processing WG 7.2 Conference, held recently in Pisa, Italy. Provides recent results as well as entirely new material on control theory and shape analysis. Written by leading authorities from various desciplines."
Download or read book Operator Semigroups Meet Complex Analysis Harmonic Analysis and Mathematical Physics written by Wolfgang Arendt and published by Birkhäuser. This book was released on 2015-12-10 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event. They will be a valuable and inspiring source of information for graduate students and established researchers.
Download or read book Inverse Problems for Partial Differential Equations written by Victor Isakov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 296 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.
