Advances In Inverse Problems For Partial Differential Equations
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Advances in Inverse Problems for Partial Differential Equations
Author: Dinh-Liem Nguyen
language: en
Publisher: American Mathematical Society
Release Date: 2023-04-12
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.
Advances in Inverse Problems for Partial Differential Equations
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 i.
Inverse Problems for Partial Differential Equations
Author: Victor Isakov
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-06-29
This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.