Inverse Problems for Partial Differential Equations

Inverse Problems for Partial Differential Equations

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 ...

Author: Victor Isakov

Publisher: Springer Science & Business Media

ISBN: 9781489900302

Category: Mathematics

Page: 286

View: 461

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.
Categories: Mathematics

Inverse Problems in Partial Differential Equations

Inverse Problems in Partial Differential Equations

David L. Colton, Richard E. Ewing, William Rundell, Society for Industrial and
Applied Mathematics ... conference on Inverse Problems in Partial Differential
Equations, part of the Summer Research Conferences in the Mathematical
Sciences, ...

Author: David L. Colton

Publisher: SIAM

ISBN: 0898712521

Category: Mathematics

Page: 214

View: 806

Categories: Mathematics

Introduction to Inverse Problems for Differential Equations

Introduction to Inverse Problems for Differential Equations

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.

Author: Alemdar Hasanov Hasanoğlu

Publisher: Springer

ISBN: 9783319627977

Category: Mathematics

Page: 261

View: 190

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.
Categories: Mathematics

Control And Inverse Problems For Partial Differential Equations

Control And Inverse Problems For Partial Differential Equations

E. Fernández-Cara and A. Münch. Numerical null controllability of semilinear 1d
heat equations: Fixed point, least squares and newton ... Inverse problems for
partial differential equations, volume 127 of Applied Mathematical Sciences.

Author: Bao Gang

Publisher: World Scientific

ISBN: 9789813276161

Category: Mathematics

Page: 264

View: 643

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.
Categories: Mathematics

Partial Differential Equations I

Partial Differential Equations I

This book is intended to be a comprehensive introduction to the subject of partial differential equations.

Author: Michael Eugene Taylor

Publisher: Springer Science & Business Media

ISBN: 0387946535

Category: Mathematics

Page: 563

View: 899

This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.
Categories: Mathematics

Ill Posed and Inverse Problems

Ill Posed and Inverse Problems

To honour him on the occasion of his 70th birthday renowned scientists in this field of mathematics, both from East and West, have contributed to this special collection of papers on ill-posed and inverse problems, which will be of interest ...

Author: Vladimir G. Romanov

Publisher: VSP

ISBN: 9067643629

Category: Science

Page: 468

View: 339

M.M. Lavrentiev is the author of many fundamental scientific results in many directions of mathematics and its applications, such as differential equations, inverse and ill-posed problems, tomography, numerical and applied mathematics. His results in the theory of inverse problems for differential equations and in tomography are well known all over the world. To honour him on the occasion of his 70th birthday renowned scientists in this field of mathematics, both from East and West, have contributed to this special collection of papers on ill-posed and inverse problems, which will be of interest to anyone working in this field.
Categories: Science

Mathematical Modelling Optimization Analytic and Numerical Solutions

Mathematical Modelling  Optimization  Analytic and Numerical Solutions

This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, ...

Author: Pammy Manchanda

Publisher: Springer Nature

ISBN: 9789811509285

Category: Mathematics

Page: 426

View: 941

This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.
Categories: Mathematics

Inverse Problems and Related Topics

Inverse Problems and Related Topics

(2) M.I. BELISHEv, Boundary control in reconstruction of manifolds and metrics (
the BC method), Inverse Problems, 13 (1997), pp. R1-R45 ... [15] V. Isakov,
Inverse Problems for Partial Differential Equations, Applied Mathematical
Sciences vol.

Author: Gen Nakamura

Publisher: CRC Press

ISBN: 1584881917

Category: Mathematics

Page: 248

View: 370

Inverse problems arise in many disciplines and hold great importance to practical applications. However, sound new methods are needed to solve these problems. Over the past few years, Japanese and Korean mathematicians have obtained a number of very interesting and unique results in inverse problems. Inverse Problems and Related Topics compiles papers authored by some of the top researchers in Korea and Japan. It presents a number of original and useful results and offers a unique opportunity to explore the current trends of research in inverse problems in these countries. Highlighting the existence and active work of several Japanese and Korean groups, it also serves as a guide to those seeking future scientific exchange with researchers in these countries.
Categories: Mathematics

Geometric Methods in Inverse Problems and PDE Control

Geometric Methods in Inverse Problems and PDE Control

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.

Author: Chrisopher B. Croke

Publisher: Springer Science & Business Media

ISBN: 9781468493757

Category: Mathematics

Page: 330

View: 717

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.
Categories: Mathematics

Partial Differential Equations

Partial Differential Equations

This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics.

Author: David Colton

Publisher: Courier Corporation

ISBN: 9780486138435

Category: Mathematics

Page: 320

View: 797

This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Features coverage of integral equations and basic scattering theory. Includes exercises, many with answers. 1988 edition.
Categories: Mathematics

Boundary Value Problems of Mathematical Physics

Boundary Value Problems of Mathematical Physics

For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical ...

Author: Ivar Stakgold

Publisher: SIAM

ISBN: 9780898714562

Category: Science

Page: 748

View: 909

For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.
Categories: Science

Linear Inverse Problems and Tikhonov Regularization

Linear Inverse Problems and Tikhonov Regularization

This is a clear example of the power of applying deep mathematical theory to solve practical problems.

Author: Mark Gockenbach

Publisher: The Mathematical Association of America

ISBN: 9780883851418

Category: Mathematics

Page: 333

View: 701

Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions. Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems. Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.
Categories: Mathematics

Perspectives in Mathematical Sciences

Perspectives in Mathematical Sciences

Chaotic dynamics for the two-component Bose-Einstein condensate system / Jibin Li -- 8. Recent developments and perspectives in nonlinear dynamics / Zengrong Liu -- 9. Mathematical aspects of the cold plasma model / Thomas H. Otway -- 10.

Author: Yisong Yang

Publisher: World Scientific

ISBN: 9789814289313

Category: Mathematics

Page: 354

View: 763

Mathematical sciences have been playing an increasingly important role in modern society. They are in high demand for investigating complex problems in physical science, environmental and geophysical sciences, materials science, life science and chemical sciences. This is a review volume on some timely and interesting topics in applied mathematical sciences. It reviews new developments and presents some future research directions in these topics. The chapters are written by reknowned experts in these fields. The volume is written with a wide audience in mind and hence will be accessible to graduate students, junior researchers and other professionals who are interested in the subject. The contributions of Professor Youzhong Guo, a leading expert in these areas, will be celebrated. An entire chapter will be devoted to his achievements. The underlying theme that binds the various chapters seamlessly is a set of dedicated ideas and techniques from partial differential equations and dynamical systems.
Categories: Mathematics

Parameter Identification and Inverse Problems in Hydrology Geology and Ecology

Parameter Identification and Inverse Problems in Hydrology  Geology and Ecology

The Workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, Karlsruhe, April 10-12, 1995, was organized to bring to gether an interdisciplinary group drawn from the areas of science, engineering and ...

Author: Johannes Gottlieb

Publisher: Springer Science & Business Media

ISBN: 9789400917040

Category: Science

Page: 302

View: 247

The Workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, Karlsruhe, April 10-12, 1995, was organized to bring to gether an interdisciplinary group drawn from the areas of science, engineering and mathematics for the following purposes: - to promote, encourage and influence more understanding and cooperation in the community of parameter identifiers from various disciplines, - to forge unity in diversity by bringing together a variety of disciplines that attempt to understand the reconstruction of inner model parameters, un known nonlinear constitutive relations, heterogeneous structures inside of geological objects, sources or sinks from observational data, - to discuss modern regularization tools for handling improperly posed pro blems and strategies of incorporating a priori knowledge from the applied problem into the model and its treatment. These proceedings contain some of the results of the workshop, representing a bal anced selection of contributions from the various groups of participants. The reviewed invited and contributed articles are grouped according to the broad headings of hydrology, non-linear diffusion and soil physics, geophysical methods, mathematical analysis of inverse and ill-posed problems and parallel algorithms for inverse problems. Some of the issues adressed by the articles in these proceedings include the rela tion between least squares and direct formulations of inverse problems for partial differential equations, nonlinear regularization, identification of nonlinear consti tutive relations, fast parallel algorithms for large scale inverse problems, reduction of model structures, geostatistical inversion techniques.
Categories: Science

Partial Differential Equations

Partial Differential Equations

This text provides an introduction to the theory of partial differential equations.

Author: Michael E. Taylor

Publisher: Springer Science & Business Media

ISBN: 0387946543

Category: Mathematics

Page: 563

View: 774

This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
Categories: Mathematics

Inverse Acoustic and Electromagnetic Scattering Theory

Inverse Acoustic and Electromagnetic Scattering Theory

As previously mentioned, for problems in mathematical physics Hadamard [118]
postulated three requirements: a solution should ... on ill-posed problems was
neglected since they were not considered relevant to the proper treatment of
applied problems. ... In particular, a large number of inverse problems for partial
differential equations turn out to be ill-posed. ... Colton and R. Kress, Inverse
Acoustic and Electromagnetic Scattering Theory, Applied Mathematical Sciences
93, DOI ...

Author: David Colton

Publisher: Springer Science & Business Media

ISBN: 9781461449416

Category: Mathematics

Page: 406

View: 329

The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory. Review of earlier editions: “Colton and Kress have written a scholarly, state of the art account of their view of direct and inverse scattering. The book is a pleasure to read as a graduate text or to dip into at leisure. It suggests a number of open problems and will be a source of inspiration for many years to come.” SIAM Review, September 1994 “This book should be on the desk of any researcher, any student, any teacher interested in scattering theory.” Mathematical Intelligencer, June 1994
Categories: Mathematics

Three Courses on Partial Differential Equations

Three Courses on Partial Differential Equations

This book provides an introduction to three different topics in partial differential equations stemming from applications. The subject of the first course is equilibrium positions of several disks rolling on a wire.

Author: Eric Sonnendrücker

Publisher: Walter de Gruyter

ISBN: 9783110179583

Category: Mathematics

Page: 162

View: 780

This book provides an introduction to three different topics in partial differential equations stemming from applications. The subject of the first course is equilibrium positions of several disks rolling on a wire. In particular, existence and uniqueness of and the exact position for an equilibrium are discussed. The second course deals with problems arising from acoustics and geophysics where waves propagate in complicated media, the properties of which can only be described statistically. It turns out that if the different scales presented in the problem can be separated, there exists a deterministic result. The third course is devoted to so-called inverse problems, where one or several parameters of a partial differential equation need to be determined by using, for instance, measurements on the boundary of the domain. The question that arises naturally is what information is necessary to determine the unknown parameters. This question is answered in different settings. The text is addressed to students and researchers with a basic background in partial differential equations.
Categories: Mathematics

Mathematics in Science and Technology

Mathematics in Science and Technology

This unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets to real world systems.

Author: A H Siddiqi

Publisher: World Scientific

ISBN: 9789814462143

Category: Mathematics

Page: 556

View: 925

This unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets to real world systems. The book provides a comprehensive overview of current research of several outstanding scholars engaged in diverse fields such as complexity theory, vertex coupling in quantum graphs, mixing of substances by turbulence, network dynamics and architecture, processes with rate — independent hysteresis, numerical analysis of Hamilton Jacobi — Bellman equations, simulations of complex stochastic differential equations, optimal flow control, shape optimal flow control, shape optimization and aircraft designing, mathematics of brain, nanotechnology and DNA structure and mathematical models of environmental problems. The volume also contains contributory talks based on current researches of comparatively young researchers participating in the conference. Contents:Part A Invited Talk:In Appreciation of Dr Zakir Husain Award (M Zuhair Nashed)Kinematical Conservation Laws (KCL): Equations of Evolution of Curves and Surfaces (K R Arun and P Prasad)Systematic Discretization of Input/Output Maps and Control of Partial Differential Equations (J Heiland, V Mehrmann and M Schmidt)Vertex Couplings in Quantum Graphs: Approximations by Scaled Schrödinger Operators (P Exner)Complexity Leads to Randomness in Chaotic Systems (R Lozi)Mathematical Modeling for Unifying Different Branches of Science, Engineering and Technology (N Rudraiah)On Equivalence Transformations and Exact Solutions of a Helmholtz Type Equation (O P Bhutani and L R Chowdhury)Cognitive Radio: State-of-the-Art and Mathematical Challenges (T Nadkar, V Thumar, A Patel, Md Z Ali Khan, U B Desai and S N Merchant)Part B Thematic Reviews:Inverse Problems of Parameter Identification in Partial Differential Equations (B Jadamba, A A Khan and M Sama)Finite Element Methods for HJB Equations (M Boulbrachene)Dynamics and Control of Underactuated Space Systems (K D Kumar and Godard)Some New Classes of Inverse Coefficient Problems in Engineering Mechanics and Computational Material Science Based on Boundary Measured Data (A Hasanov)Some Recent Developments on Mathematical Aspect of Wavelets (P Manchanda and Meenakshi)Relevance of Wavelets and Inverse Problems to Brain (A H Siddiqi, H K Sevindir, Z Aslan and C Yazici)Wavelets and Inverse Problems (K Goyal and M Mehra)Optimization Models for a Class of Structured Stochastic Games (S K Neogy, S Sinha, A K Das and A Gupta)Part C Contributory Talks:Predator-Prey Relations for Mammals where Prey Suppress Breeding (Q J Khan and M Al-Lawatia)SEI Model with Varying Transmission and Mortality Rates (G Rost)Trajectories and Stability Regions of the Lagrangian Points in the Generalized Chermnykh-Like Problem (B S Kushvah)MHD Flow Past an Infinite Plate Under the Effect of Gravity Modulation (S Wasu and S C Rajvanshi) Readership: Researchers in mathematical modeling, numerical analysis and computational mathematics. Keywords:Complexity Theory;Vertex Coupling in Quantum Graphs;Hamilton-Jacobi–Bellman Equation;Prey and Predator Model;Inverse Problems and Wavelets;Dynamics and Control of Under Actuated Space Systems
Categories: Mathematics