Ill-posed Problems of Mathematical Physics and Analysis
Author: Mikhail Mikhaĭlovich Lavrentʹev
Publisher: Providence, R.I. : American Mathematical Society
Published: 1986
Total Pages: 304
ISBN-13:
DOWNLOAD EBOOK →Author: Mikhail Mikhaĭlovich Lavrentʹev
Publisher: Providence, R.I. : American Mathematical Society
Published: 1986
Total Pages: 304
ISBN-13:
DOWNLOAD EBOOK →Author: Mikhail Mikha_lovich Lavrent_ev
Publisher: American Mathematical Soc.
Published: 1986-12-31
Total Pages: 300
ISBN-13: 9780821898147
DOWNLOAD EBOOK →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: Mikhail Mikhailovich Lavrent'ev
Publisher:
Published: 1986
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOK →Author: Mikhail Mikhaĭlovich Lavrentʹev
Publisher:
Published: 1986
Total Pages: 298
ISBN-13: 9781470444785
DOWNLOAD EBOOK →Author: Mikhail M. Lavrent'ev
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2014-07-24
Total Pages: 216
ISBN-13: 3110936526
DOWNLOAD EBOOK →These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis", held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences
Author: V.A. Morozov
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 275
ISBN-13: 1461252806
DOWNLOAD EBOOK →Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.
Author: Mikhail M. Lavrent'ev
Publisher: V.S.P. International Science
Published: 2003
Total Pages: 205
ISBN-13: 9789067643801
DOWNLOAD EBOOK →These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis", held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences
Author: A. A. Samarskii
Publisher: Walter de Gruyter
Published: 2008-08-27
Total Pages: 453
ISBN-13: 3110205793
DOWNLOAD EBOOK →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: Sergey I. Kabanikhin
Publisher: Walter de Gruyter
Published: 2011-12-23
Total Pages: 476
ISBN-13: 3110224011
DOWNLOAD EBOOK →The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject.
Author: Mikhail M. Lavrent'ev
Publisher: Walter de Gruyter
Published: 2012-05-07
Total Pages: 288
ISBN-13: 3110915529
DOWNLOAD EBOOK →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.