Inverse Problems for Partial Differential Equations

Author: Victor Isakov

Publisher: Springer Science & Business Media

ISBN: 1489900306

Category: Mathematics

Page: 286

View: 6295

DOWNLOAD NOW »

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.
Release

Inverse Problems and Applications

Author: Plamen Stefanov,András Vasy,Maciej Zworski

Publisher: American Mathematical Soc.

ISBN: 1470410796

Category: Mathematics

Page: 309

View: 1757

DOWNLOAD NOW »

This volume contains the proceedings of two conferences on Inverse Problems and Applications, held in 2012, to celebrate the work of Gunther Uhlmann. The first conference was held at the University of California, Irvine, from June 18-22, 2012, and the second was held at Zhejiang University, Hangzhou, China, from September 17-21, 2012. The topics covered include inverse problems in medical imaging, scattering theory, geometry and image processing, and the mathematical theory of cloaking, as well as methods related to inverse problems.
Release

Modern Aspects of the Theory of Partial Differential Equations

Author: Michael Ruzhansky,Jens Wirth

Publisher: Springer Science & Business Media

ISBN: 9783034800693

Category: Mathematics

Page: 368

View: 5069

DOWNLOAD NOW »

The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.
Release

Partial Differential Equations I

Basic Theory

Author: Michael Eugene Taylor,Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 9780387946535

Category: Mathematics

Page: 563

View: 1662

DOWNLOAD NOW »

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.
Release

Inverse Problems and Related Topics

Author: Gen Nakamura,Saburou Saitoh,Jin Kean Seo

Publisher: CRC Press

ISBN: 9781584881919

Category: Mathematics

Page: 248

View: 8415

DOWNLOAD NOW »

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.
Release

Introduction to Inverse Problems for Differential Equations

Author: Alemdar Hasanov Hasanoğlu,Vladimir G. Romanov

Publisher: Springer

ISBN: 331962797X

Category: Mathematics

Page: 261

View: 1158

DOWNLOAD NOW »

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.
Release

Perspectives in Mathematical Sciences

Author: Yisong Yang,Xinchu Fu,Jinqiao Duan

Publisher: World Scientific

ISBN: 9814289310

Category: Mathematics

Page: 354

View: 2346

DOWNLOAD NOW »

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.
Release

Partial Differential Equations

Basic Theory

Author: Michael E. Taylor

Publisher: Springer Science & Business Media

ISBN: 9780387946542

Category: Mathematics

Page: 563

View: 3468

DOWNLOAD NOW »

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.
Release

Partial Differential Equations

Analytical and Numerical Methods, Second Edition

Author: Mark S. Gockenbach

Publisher: SIAM

ISBN: 0898719356

Category: Mathematics

Page: 654

View: 1110

DOWNLOAD NOW »

A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.
Release