Author: Michail M. Lavrentiev
Publisher: Springer Science & Business Media
ISBN: 3642882102
Category : Science
Languages : en
Pages : 115
Get Book Here
Book Description
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 . . . . . . .
Author: V.A. Morozov
Publisher: Springer Science & Business Media
ISBN: 1461252806
Category : Mathematics
Languages : en
Pages : 275
Get Book Here
Book Description
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: L. E. Payne
Publisher: SIAM
ISBN: 9781611970463
Category : Mathematics
Languages : en
Pages : 81
Get Book Here
Book Description
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.
Author: Robert J. Sacker
Publisher:
ISBN:
Category :
Languages : en
Pages : 88
Get Book Here
Book Description
Author: Karl-Heinz Hoffmann
Publisher: Birkhäuser
ISBN: 3034882335
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.
Author: Victor Isakov
Publisher: American Mathematical Soc.
ISBN: 0821815326
Category : Mathematics
Languages : en
Pages : 209
Get Book Here
Book Description
A careful exposition of a research field of current interest. This includes a brief survey of the subject and an introduction to recent developments and unsolved problems.
Author: V. G. Romanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110926016
Category : Mathematics
Languages : en
Pages : 248
Get Book Here
Book Description
No detailed description available for "Inverse Problems of Mathematical Physics".
Author: Henryk Gzyl
Publisher: World Scientific
ISBN: 9814462160
Category : Mathematics
Languages : en
Pages : 351
Get Book Here
Book Description
The book describes a useful tool for solving linear inverse problems subject to convex constraints. The method of maximum entropy in the mean automatically takes care of the constraints. It consists of a technique for transforming a large dimensional inverse problem into a small dimensional non-linear variational problem.A variety of mathematical aspects of the maximum entropy method are explored as well.
Author: Pierluigi Colli
Publisher: Birkhäuser
ISBN: 3034878931
Category : Mathematics
Languages : en
Pages : 342
Get Book Here
Book Description
Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.
Author: Zenon Mróz
Publisher: Springer Science & Business Media
ISBN: 3211381341
Category : Technology & Engineering
Languages : en
Pages : 343
Get Book Here
Book Description
The nature and the human creations are full of complex phenomena, which sometimes can be observed but rarely follow our hypotheses. The best we can do is to build a parametric model and then try to adjust the unknown parameters based on the available observations. This topic, called parameter identification, is discussed in this book for materials and structures. The present volume of lecture notes follows a very successful advanced school, which we had the honor to coordinate in Udine, October 6-10, 2003. The authors of this volume present a wide spectrum of theories, methods and applications related to inverse and parameter identification problems. We thank the invited lecturers and the authors of this book for their contributions, the participants of the course for their active participation and the interesting discussions as well as the people of CISMfor their hospitality and their well-known professional help. Zenon Mroz Georgios E. Stavroulakis CONTENTS Preface An overview of enhanced modal identification by L. Bolognini 1 The reciprocity gap functional for identifying defects and cracks by H. D. Bui, A. Constantinescu and H. Maigre 17 Some innovative industrial prospects centered on inverse analyses by G. Maier, M. Bocciarelli andR. Fedele 55 Identification of damage in beam and plate structures using parameter dependent modal changes and thermographic methods by Z. Mroz andK. Dems 95 Crack and flaw identification in statics and dynamics, using filter algorithms and soft computing by G. E, Stavroulakis, M. Engelhardt andH.
