Forward And Inverse Problems For Hyperbolic Elliptic And Mixed Type Equations

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Forward And Inverse Problems For Hyperbolic Elliptic And Mixed Type Equations

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Author : Alexander G. Megrabov
language : en
Publisher: Walter de Gruyter
Release Date : 2012-05-24

Forward And Inverse Problems For Hyperbolic Elliptic And Mixed Type Equations written by Alexander G. Megrabov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.

Inverse problems are an important and rapidly developing direction in mathematics, mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monograph direct and inverse problems for partial differential equations are considered. The type of equations focused are hyperbolic, elliptic, and mixed (elliptic-hyperbolic). The direct problems arise as generalizations of problems of scattering plane elastic or acoustic waves from inhomogeneous layer (or from half-space). The inverse problems are those of determination of medium parameters by giving the forms of incident and reflected waves or the vibrations of certain points of the medium. The method of research of all inverse problems is spectral-analytical, consisting in reducing the considered inverse problems to the known inverse problems for the Sturm-Liouville equation or the string equation. Besides the book considers discrete inverse problems. In these problems an arbitrary set of point sources (emissive sources, oscillators, point masses) is determined.

Operator Theory And Ill Posed Problems

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Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22

Operator Theory And Ill Posed Problems written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.

This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.

Operator Theory And Differential Equations

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Author : Anatoly G. Kusraev
language : en
Publisher: Springer Nature
Release Date : 2021-01-13

Operator Theory And Differential Equations written by Anatoly G. Kusraev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-13 with Mathematics categories.

This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July 2019. Intended for mathematicians specializing in operator theory, functional spaces, differential equations or mathematical modeling, the book provides a state-of-the-art account of various fascinating areas of operator theory, ranging from various classes of operators (positive operators, convolution operators, backward shift operators, singular and fractional integral operators, partial differential operators) to important applications in differential equations, inverse problems, approximation theory, metric theory of surfaces, the Hubbard model, social stratification models, and viscid incompressible fluids.

Inverse Problems Of Mathematical Physics

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Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter
Release Date : 2012-05-07

Inverse Problems Of Mathematical Physics written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-07 with Mathematics categories.

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.

Ill Posed Boundary Value Problems

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Author : Serikkali E. Temirbolat
language : en
Publisher: Walter de Gruyter
Release Date : 2012-06-04

Ill Posed Boundary Value Problems written by Serikkali E. Temirbolat and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-04 with Mathematics categories.

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.

Characterisation Of Bio Particles From Light Scattering

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Author : Valeri P. Maltsev
language : en
Publisher: Walter de Gruyter
Release Date : 2013-03-01

Characterisation Of Bio Particles From Light Scattering written by Valeri P. Maltsev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with Mathematics categories.

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.

Counterexamples In Optimal Control Theory

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Author : Semen Ya. Serovaiskii
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-01

Counterexamples In Optimal Control Theory written by Semen Ya. Serovaiskii and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-01 with Mathematics categories.

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.

Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis

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Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-07-24

Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis written by Mikhail M. Lavrent'ev 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 2014-07-24 with Mathematics categories.

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

Forward And Inverse Problems For Hyperbolic Elliptic And Mixed Type Equations

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Author : A. G. Megrabov
language : en
Publisher:
Release Date :

Forward And Inverse Problems For Hyperbolic Elliptic And Mixed Type Equations written by A. G. Megrabov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Linear Sobolev Type Equations And Degenerate Semigroups Of Operators

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Author : Georgy A. Sviridyuk
language : en
Publisher: Walter de Gruyter
Release Date : 2012-06-04

Linear Sobolev Type Equations And Degenerate Semigroups Of Operators written by Georgy A. Sviridyuk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-04 with Mathematics categories.

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.