Numerical Methods for Solving Inverse Problems of Mathematical Physics PDF Download

Author: A. A. Samarskii
Publisher: Walter de Gruyter
ISBN: 3110205793
Category : Mathematics
Languages : en
Pages : 453

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Book Description
The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

Author: Alexander A. Samarskii
Publisher:
ISBN: 9789004155237
Category : Differential equations, Partial
Languages : en
Pages : 450

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Book Description
This book treats some particular inverse problems for time-dependent and time-independent equations often encountered in mathematical physics.

Author: Global Express Ltd. Co.
Publisher: CRC Press
ISBN: 9780824719876
Category : Mathematics
Languages : en
Pages : 736

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Book Description
Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.

Author: Mikhail M. Lavrent'ev
Publisher: Walter de Gruyter
ISBN: 3110915529
Category : Mathematics
Languages : en
Pages : 288

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Book Description
This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Author: Alexander G. Ramm
Publisher: Springer Science & Business Media
ISBN: 0387232184
Category : Technology & Engineering
Languages : en
Pages : 442

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Book Description
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Author: Mathias Richter
Publisher: Springer Nature
ISBN: 3030593177
Category : Mathematics
Languages : en
Pages : 281

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Book Description
This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required. Containing up-to-date methods, this book will provide readers with the tools necessary to compute regularized solutions of inverse problems. A variety of practical examples from geophysics are used to motivate the presentation of abstract mathematical ideas, thus assuring an accessible approach. Beginning with four examples of inverse problems, the opening chapter establishes core concepts, such as formalizing these problems as equations in vector spaces and addressing the key issue of ill-posedness. Chapter Two then moves on to the discretization of inverse problems, which is a prerequisite for solving them on computers. Readers will be well-prepared for the final chapters that present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems. Model problems reflecting scenarios of practical interest in the geosciences, such as inverse gravimetry and full waveform inversion, are fully worked out throughout the book. They are used as test cases to illustrate all single steps of solving inverse problems, up to numerical computations. Five appendices include the mathematical foundations needed to fully understand the material. This second edition expands upon the first, particularly regarding its up-to-date treatment of nonlinear problems. Following the author’s approach, readers will understand the relevant theory and methodology needed to pursue more complex applications. Inverse Problems is ideal for graduate students and researchers interested in geophysics and geosciences.

Author: V. G. Romanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110926016
Category : Mathematics
Languages : en
Pages : 248

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Book Description
No detailed description available for "Inverse Problems of Mathematical Physics".

Author: Mikhail Mikha_lovich Lavrent_ev
Publisher: American Mathematical Soc.
ISBN: 9780821898147
Category : Mathematics
Languages : en
Pages : 300

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Book Description
Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential equations

Author: R.P. Gilbert
Publisher: Springer Science & Business Media
ISBN: 9780792360056
Category : Mathematics
Languages : en
Pages : 466

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Book Description
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.

Author: Larisa Beilina
Publisher: Springer Nature
ISBN: 3030486346
Category : Mathematics
Languages : en
Pages : 147

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Book Description
This proceedings volume gathers peer-reviewed, selected papers presented at the “Mathematical and Numerical Approaches for Multi-Wave Inverse Problems” conference at the Centre Internacional de Rencontres Mathématiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems. Multi-wave inverse problems have a wide range of applications in acoustics, electromagnetics, optics, medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse problems are both nonlinear and ill-posed: two factors that pose major challenges for the development of new numerical methods for solving these problems, which are discussed in detail. These papers will be of interest to all researchers and graduate students working in the fields of nonlinear and inverse problems and its applications.