Inverse And Improperly Posed Problems In Differential Equations
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Improperly Posed Problems In Partial Differential Equations
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Author : L. E. Payne
language : en
Publisher: SIAM
Release Date : 1975-01-01
Improperly Posed Problems In Partial Differential Equations written by L. E. Payne and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-01-01 with Mathematics categories.
Improperly posed Cauchy problems are the primary topics in this discussion which assumes that the geometry and coefficients of the equations are known precisely. Appropriate references are made to other classes of improperly posed problems. The contents include straight forward examples of methods eigenfunction, quasireversibility, logarithmic convexity, Lagrange identity, and weighted energy used in treating improperly posed Cauchy problems. The Cauchy problem for a class of second order operator equations is examined as is the question of determining explicit stability inequalities for solving the Cauchy problem for elliptic equations. Among other things, an example with improperly posed perturbed and unperturbed problems is discussed and concavity methods are used to investigate finite escape time for classes of operator equations.
Inverse Problems In Differential Equations
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Author : G. Anger
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1990-12-31
Inverse Problems In Differential Equations written by G. Anger and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-31 with Mathematics categories.
No detailed description available for "Inverse Problems in Differential Equations".
Inverse And Improperly Posed Problems In Differential Equations
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Author : G. Anger
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-01-19
Inverse And Improperly Posed Problems In Differential Equations written by G. Anger and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-19 with Mathematics categories.
No detailed description available for "Inverse and Improperly Posed Problems in Differential Equations".
Some Improperly Posed Problems Of Mathematical Physics
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Author : Michail M. Lavrentiev
language : en
Publisher: Springer
Release Date : 2012-04-19
Some Improperly Posed Problems Of Mathematical Physics written by Michail M. Lavrentiev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-19 with Science categories.
This monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard. The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation. The second part deals with a number of problems of analytic continuations of analytic and harmonic functions. The third part is concerned with the investigation of the so-called inverse problems for differential equations in which it is required to determine a dif ferential equation from a certain family of its solutions. Novosibirsk June, 1967 M. M. LAVRENTIEV Table of Contents Chapter I Formu1ation of some Improperly Posed Problems of Mathematic:al Physics § 1 Improperly Posed Problems in Metric Spaces. . . . . . . . . § 2 A Probability Approach to Improperly Posed Problems. . . 8 Chapter II Analytic Continuation § 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 § 2 The Cauchy Problem for the Laplace Equation . . . . . . . 18 § 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity. . . . . . . . . . . . . 22 § 4 Analytic Continuation of a Function of Two Real Variables 32 § 5 Analytic Continuation of Harmonic Functions from a Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 § 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter III Inverse Problems for Differential Equations § 1 The Inverse Problem for a Newtonian Potential . . . . . . .
Inverse And Improperly Posed Problems In Differential Equations
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Author : Martin-Luther-Universität Halle-Wittenberg. Department of Mathematics
language : en
Publisher:
Release Date :
Inverse And Improperly Posed Problems In Differential Equations written by Martin-Luther-Universität Halle-Wittenberg. Department of Mathematics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Inverse Problems Of Mathematical Physics
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Author : V. G. Romanov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05
Inverse Problems Of Mathematical Physics written by V. G. Romanov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
No detailed description available for "Inverse Problems of Mathematical Physics".
Some Improperly Posed Problems Of Mathematical Physics
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Author : Michail M. Lavrentiev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Some Improperly Posed Problems Of Mathematical Physics written by Michail M. Lavrentiev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-13 with Science categories.
This monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard. The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation. The second part deals with a number of problems of analytic continuations of analytic and harmonic functions. The third part is concerned with the investigation of the so-called inverse problems for differential equations in which it is required to determine a dif ferential equation from a certain family of its solutions. Novosibirsk June, 1967 M. M. LAVRENTIEV Table of Contents Chapter I Formu1ation of some Improperly Posed Problems of Mathematic:al Physics § 1 Improperly Posed Problems in Metric Spaces. . . . . . . . . § 2 A Probability Approach to Improperly Posed Problems. . . 8 Chapter II Analytic Continuation § 1 Analytic Continuation of a Function of One Complex Variable from a Part of the Boundary of the Region of Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 § 2 The Cauchy Problem for the Laplace Equation . . . . . . . 18 § 3 Determination of an Analytic Function from its Values on a Set Inside the Domain of Regularity. . . . . . . . . . . . . 22 § 4 Analytic Continuation of a Function of Two Real Variables 32 § 5 Analytic Continuation of Harmonic Functions from a Circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 § 6 Analytic Continuation of Harmonic Function with Cylin drical Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter III Inverse Problems for Differential Equations § 1 The Inverse Problem for a Newtonian Potential . . . . . . .
Inverse Problems In Quantum Scattering Theory
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Author : Khosrow Chadan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inverse Problems In Quantum Scattering Theory written by Khosrow Chadan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.
Inverse Scattering Problems In Optics
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Author : H.P. Baltes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inverse Scattering Problems In Optics written by H.P. Baltes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
When, in the spring of 1979, H.P. Baltes presented me with the precursor of this vo 1 ume, the book on "Inverse Source Problems in Opti cs", I expressed my gratitude in a short note, 11hich in translation, reads: "Dear Dr. Ba ltes, the mere titl e of your unexpected gift evokes memori es of a period, which, in the terminology of your own contribution, would be described as the Stone Age of the Inverse Problem. Those were pleasant times. Walter Kohn and I lived in a cave by ourselves, drew pictures on the walls, and nobody seemed to care. Now, however, Inversion has become an Industry, which I contemplate with as much bewilderment as a surviving Tasmanian aborigine gazing at a modern oil refinery with its towers, its fl ares, and the confus i ng maze of its tubes." The present volume makes me feel even more aboriginal - impossible for me to fathom its content. What I can point out, however, is one of the forgotten origins of the Inverse Scattering Problem of Quantum Mechanics: Werner Heisenberg's "S-Matrix Theory" of 1943. This grandiose scheme had the purpose of eliminating the notion of the Hamiltonian in favour of the scattering operator. If Successful, it would have done away once and for all with any kind of inverse problem.
Inverse Problems In Diffusion Processes
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Author : Heinz W. Engl
language : en
Publisher: SIAM
Release Date : 1995-01-01
Inverse Problems In Diffusion Processes written by Heinz W. Engl and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
This collection of expository papers encompasses both the theoretical and physical application side of inverse problems in diffusion processes.