An Introduction to Identification Problems via Functional Analysis
An Introduction to Identification Problems via Functional Analysis

Author: Alfredo Lorenzi

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-07-24

Total Pages: 256

ISBN-13: 3110940922

DOWNLOAD EBOOK

this monograph is based on two courses in computational mathematics and operative research, which were given by the author in recent years to doctorate and PhD students. The text focuses on an aspect of the theory of inverse problems, which is usually referred to as identification of parameters (numbers, vectors, matrices, functions) appearing in differential – or integrodifferential – equations. The parameters of such equations are either quite unknown or partially unknown, however knowledge about these is usually essential as they describe the intrinsic properties of the material or substance under consideration.

Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis
Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis

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

Inverse Problems of Mathematical Physics
Inverse Problems of Mathematical Physics

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.

Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

Author: Sergey I. Kabanikhin

Publisher: Walter de Gruyter

Published: 2013-04-09

Total Pages: 188

ISBN-13: 3110960710

DOWNLOAD EBOOK

The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

Ill-Posed Boundary-Value Problems
Ill-Posed Boundary-Value Problems

Author: Serikkali E. Temirbolat

Publisher: Walter de Gruyter

Published: 2012-06-04

Total Pages: 152

ISBN-13: 3110915510

DOWNLOAD EBOOK

This monograph extends well-known facts to new classes of problems and works out novel approaches to the solution of these problems. It is devoted to the questions of ill-posed boundary-value problems for systems of various types of the first-order differential equations with constant coefficients and the methods for their solution.

Well-posed, Ill-posed, and Intermediate Problems with Applications
Well-posed, Ill-posed, and Intermediate Problems with Applications

Author: Petrov Yuri P.

Publisher: Walter de Gruyter

Published: 2011-12-22

Total Pages: 245

ISBN-13: 3110195305

DOWNLOAD EBOOK

This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.

Carleman Estimates for Coefficient Inverse Problems and Numerical Applications
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications

Author: Michael V. Klibanov

Publisher: Walter de Gruyter

Published: 2012-04-17

Total Pages: 292

ISBN-13: 3110915545

DOWNLOAD EBOOK

In this monograph, the main subject of the author's considerations is coefficient inverse problems. Arising in many areas of natural sciences and technology, such problems consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals. Although the authors pay strong attention to the rigorous justification of known results, they place the primary emphasis on new concepts and developments.

Counterexamples in Optimal Control Theory
Counterexamples in Optimal Control Theory

Author: Semen Ya. Serovaiskii

Publisher: Walter de Gruyter

Published: 2011-12-01

Total Pages: 185

ISBN-13: 3110915537

DOWNLOAD EBOOK

This monograph deals with cases where optimal control either does not exist or is not unique, cases where optimality conditions are insufficient of degenerate, or where extremum problems in the sense of Tikhonov and Hadamard are ill-posed, and other situations. A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect. The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems.

Characterisation of Bio-Particles from Light Scattering
Characterisation of Bio-Particles from Light Scattering

Author: Valeri P. Maltsev

Publisher: Walter de Gruyter

Published: 2013-03-01

Total Pages: 144

ISBN-13: 3110915553

DOWNLOAD EBOOK

The primary aim of this monograph is to provide a systematic state-of-the-art summary of the light scattering of bioparticles, including a brief consideration of analytical and numerical methods for computing electromagnetic scattering by single particles, a detailed discussion of the instrumental approach used in measurement of light scattering, an analysis of the methods used in solution of the inverse light scattering problem, and an introduction of the results dealing with practical analysis of biosamples. Considering the widespread need for this information in optics, remote sensing, engineering, medicine, and biology, the book is useful to many graduate students, scientists, and engineers working on various aspects of electromagnetic scattering and its applications.

Linear Sobolev Type Equations and Degenerate Semigroups of Operators
Linear Sobolev Type Equations and Degenerate Semigroups of Operators

Author: Georgy A. Sviridyuk

Publisher: Walter de Gruyter

Published: 2012-06-04

Total Pages: 224

ISBN-13: 3110915502

DOWNLOAD EBOOK

Focusing on the mathematics, and providing only a minimum of explicatory comment, this volume contains six chapters covering auxiliary material, relatively p-radial operators, relatively p-sectorial operators, relatively σ-bounded operators, Cauchy problems for inhomogenous Sobolev-type equations, bounded solutions to Sobolev-type equations, and optimal control.