Control And Inverse Problems For Partial Differential Equations

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Control And Inverse Problems For Partial Differential Equations

Author : Bao Gang
Publisher : World Scientific
ISBN 13 : 9813276169
Total Pages : 264 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Control And Inverse Problems For Partial Differential Equations by : Bao Gang

Download or read book Control And Inverse Problems For Partial Differential Equations written by Bao Gang and published by World Scientific. This book was released on 2019-04-08 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes for the LIASFMA Hangzhou Autumn School on 'Control and Inverse Problems for Partial Differential Equations' which was held during October 17-22, 2016 at Zhejiang University, Hangzhou, China. This autumn school is one of the activities organized by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA). Established jointly by eight institutions in China and France in 2014, LIASFMA aims at providing a platform for many leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in broad areas of applied mathematics.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in control and inverse problems. And the readers are exposed not only to the basic theories and methods but also to the forefront of research directions in both fields.

Advances in Inverse Problems for Partial Differential Equations

Author : Dinh-Liem Nguyen
Publisher : American Mathematical Society
ISBN 13 : 1470469685
Total Pages : 218 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Advances in Inverse Problems for Partial Differential Equations by : Dinh-Liem Nguyen

Download or read book Advances in Inverse Problems for Partial Differential Equations written by Dinh-Liem Nguyen and published by American Mathematical Society. This book was released on 2023-04-12 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of two AMS Special Sessions “Recent Developments on Analysis and Computation for Inverse Problems for PDEs,” virtually held on March 13–14, 2021, and “Recent Advances in Inverse Problems for Partial Differential Equations,” virtually held on October 23–24, 2021. The papers in this volume focus on new results on numerical methods for various inverse problems arising in electrical impedance tomography, inverse scattering in radar and optics problems, reconstruction of initial conditions, control of acoustic fields, and stock price forecasting. The authors studied iterative and non-iterative approaches such as optimization-based, globally convergent, sampling, and machine learning-based methods. The volume provides an interesting source on advances in computational inverse problems for partial differential equations.

Inverse Problems in Partial Differential Equations

Author : David L. Colton
Publisher : SIAM
ISBN 13 : 9780898712520
Total Pages : 234 pages
Book Rating : 4.7/5 (125 download)

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Book Synopsis Inverse Problems in Partial Differential Equations by : David L. Colton

Download or read book Inverse Problems in Partial Differential Equations written by David L. Colton and published by SIAM. This book was released on 1990-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Deterministic and Stochastic Optimal Control and Inverse Problems

Author : Baasansuren Jadamba
Publisher : CRC Press
ISBN 13 : 1000511758
Total Pages : 378 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Deterministic and Stochastic Optimal Control and Inverse Problems by : Baasansuren Jadamba

Download or read book Deterministic and Stochastic Optimal Control and Inverse Problems written by Baasansuren Jadamba and published by CRC Press. This book was released on 2021-12-15 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.

Inverse Problems for Partial Differential Equations

Author : Victor Isakov
Publisher : Springer Science & Business Media
ISBN 13 : 1489900306
Total Pages : 296 pages
Book Rating : 4.4/5 (899 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 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.

Inverse Problems for Fractional Partial Differential Equations

Author : Barbara Kaltenbacher
Publisher : American Mathematical Society
ISBN 13 : 1470472775
Total Pages : 522 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Inverse Problems for Fractional Partial Differential Equations by : Barbara Kaltenbacher

Download or read book Inverse Problems for Fractional Partial Differential Equations written by Barbara Kaltenbacher and published by American Mathematical Society. This book was released on 2023-07-13 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters. The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case. The book also has an extensive historical section and the material that can be called "fractional calculus" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.

Geometric Methods in Inverse Problems and PDE Control

Author : Chrisopher B. Croke
Publisher : Springer Science & Business Media
ISBN 13 : 1468493752
Total Pages : 334 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Geometric Methods in Inverse Problems and PDE Control by : Chrisopher B. Croke

Download or read book Geometric Methods in Inverse Problems and PDE Control written by Chrisopher B. Croke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.

Inverse Problems and Related Topics

Author : Jin Cheng
Publisher : Springer Nature
ISBN 13 : 9811515921
Total Pages : 310 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Inverse Problems and Related Topics by : Jin Cheng

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.

Introduction to Inverse Problems for Differential Equations

Author : Alemdar Hasanov Hasanoğlu
Publisher : Springer Nature
ISBN 13 : 303079427X
Total Pages : 521 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Introduction to Inverse Problems for Differential Equations by : Alemdar Hasanov Hasanoğlu

Download or read book Introduction to Inverse Problems for Differential Equations written by Alemdar Hasanov Hasanoğlu and published by Springer Nature. This book was released on 2021-08-02 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.

Optimization and Control for Partial Differential Equations

Author : Roland Herzog
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110695987
Total Pages : 474 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Optimization and Control for Partial Differential Equations by : Roland Herzog

Download or read book Optimization and Control for Partial Differential Equations written by Roland Herzog and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-07 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Numerical Treatment of Inverse Problems in Differential and Integral Equations

Author : Deuflhard
Publisher : Springer Science & Business Media
ISBN 13 : 1468473247
Total Pages : 369 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Numerical Treatment of Inverse Problems in Differential and Integral Equations by : Deuflhard

Download or read book Numerical Treatment of Inverse Problems in Differential and Integral Equations written by Deuflhard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many scientific or engineering applications, where ordinary differen tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas ured data and an associated theoretical model, determine unknown para meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen sitivity coefficients for the model. may be rather time and storage con suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev itable discretization errors, regularization techniques are necessary.

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.

Direct and Inverse Problems of Mathematical Physics

Author : R.P. Gilbert
Publisher : Springer Science & Business Media
ISBN 13 : 1475732147
Total Pages : 452 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Direct and Inverse Problems of Mathematical Physics by : R.P. Gilbert

Download or read book Direct and Inverse Problems of Mathematical Physics written by R.P. Gilbert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of papers presented in the special sessions on "Wave Phenomena and Related Topics", and "Asymptotics and Homogenization" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT -9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the 'participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense. This volume has the title Direct and Inverse Problems of Mathematical Physics which consists of the papers on scattering theory, coefficient identification, uniqueness and existence theorems, boundary controllability, wave propagation in stratified media, viscous flows, nonlinear acoustics, Sobolev spaces, singularity theory, pseudo differential operators, and semigroup theory.

Inverse Problems in Differential Equations

Author : G. Anger
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112707176
Total Pages : 256 pages
Book Rating : 4.1/5 (127 download)

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Book Synopsis Inverse Problems in Differential Equations by : G. Anger

Download or read book Inverse Problems in Differential Equations written by G. Anger and published by Walter de Gruyter GmbH & Co KG. This book was released on 1990-12-31 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Inverse Problems in Differential Equations".

Inverse Problems for Partial Differential Equations

Author : Yu. Ya Belov
Publisher : V.S.P. International Science
ISBN 13 : 9789067643580
Total Pages : 211 pages
Book Rating : 4.6/5 (435 download)

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Book Synopsis Inverse Problems for Partial Differential Equations by : Yu. Ya Belov

Download or read book Inverse Problems for Partial Differential Equations written by Yu. Ya Belov and published by V.S.P. International Science. This book was released on 2002 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to identification problems of coefficients in equations of mathematical physics. It invesitgates the existence and uniqueness of the solutions for identification coefficient problems in parabolic and hyperbolic equations and equation systems of composite type. The problems are studied with the Cauchy data and equations in which the Fourier transform with respect to the chosen variable is supposed to occur. Differential properties of the solutions for the original direct problems and their behavior under great values of time are studied on the basis of solution properties for direct problems. The identification problems with one or two unknown coefficients are also investigated. For initial boundary value conditions linear and nonlinear parabolic equations are studied.

Partial Differential Equations and Inverse Problems

Author : Carlos Conca
Publisher : American Mathematical Soc.
ISBN 13 : 9780821856970
Total Pages : 428 pages
Book Rating : 4.8/5 (569 download)

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Book Synopsis Partial Differential Equations and Inverse Problems by : Carlos Conca

Download or read book Partial Differential Equations and Inverse Problems written by Carlos Conca and published by American Mathematical Soc.. This book was released on 2004-09-22 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of articles from the Proceedings of the Pan-American Advanced Studies Institute reflects recent developments in partial differential equations, nonlinear analysis and inverse problems. Interactions among these topics have produced remarkable developments over the last couple of decades. This volume contains survey articles reflecting the work of leading experts who presented minicourses at the event. Contributors include J. Busca, Y. Capdeboscq, M.S. Vogelius, F. A. Grunbaum, L. F. Matusevich, M. de Hoop, and P. Kuchment. The volume is suitable for graduate students and researchers interested in partial differential equations and their applications in nonlinear analysis and inverse problems.

Controllability of Partial Differential Equations Governed by Multiplicative Controls

Author : Alexander Y. Khapalov
Publisher : Springer
ISBN 13 : 3642124135
Total Pages : 296 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Controllability of Partial Differential Equations Governed by Multiplicative Controls by : Alexander Y. Khapalov

Download or read book Controllability of Partial Differential Equations Governed by Multiplicative Controls written by Alexander Y. Khapalov and published by Springer. This book was released on 2010-05-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The methodology is illustrated with a variety of model equations.