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Ill Posed Internal Boundary Value Problems For The Biharmonic Equation
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Book Synopsis Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation by : Mukarram A. Atakhodzhaev
Download or read book Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation written by Mukarram A. Atakhodzhaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Internal boundary value problems deals with the problem of determining the solution of an equation if data are given on two manifolds. One manifold is the domain boundary and the other manifold is situated inside the domain. This monograph studies three essentially ill-posed internal boundary value problems for the biharmonic equation and the Cauchy problem for the abstract biharmonic equation, both qualitatively and quantitatively. In addition, some variants of these problems and the Cauchy problem, as well as the m-dimensional case, are considered. The author introduces some new notions, such as the notion of complete solvability.
Book Synopsis Ill-Posed Boundary-Value Problems by : Serikkali E. Temirbolat
Download or read book Ill-Posed Boundary-Value Problems written by Serikkali E. Temirbolat and published by Walter de Gruyter. This book was released on 2012-06-04 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operator Theory and Ill-Posed Problems by : Mikhail M. Lavrent'ev
Download or read book Operator Theory and Ill-Posed Problems written by Mikhail M. Lavrent'ev and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Well-posed, Ill-posed, and Intermediate Problems with Applications by : Petrov Yuri P.
Download or read book Well-posed, Ill-posed, and Intermediate Problems with Applications written by Petrov Yuri P. and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Linear Ill-Posed Problems and its Applications by : Valentin K. Ivanov
Download or read book Theory of Linear Ill-Posed Problems and its Applications written by Valentin K. Ivanov and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a revised and extended version of the Russian edition from 1978. It includes the general theory of linear ill-posed problems concerning e. g. the structure of sets of uniform regularization, the theory of error estimation, and the optimality method. As a distinguishing feature the book considers ill-posed problems not only in Hilbert but also in Banach spaces. It is natural that since the appearance of the first edition considerable progress has been made in the theory of inverse and ill-posed problems as wall as in ist applications. To reflect these accomplishments the authors included additional material e. g. comments to each chapter and a list of monographs with annotations.
Book Synopsis Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis by : Mikhail M. Lavrent'ev
Download or read book Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis written by Mikhail M. Lavrent'ev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Counterexamples in Optimal Control Theory by : Semen Ya. Serovaiskii
Download or read book Counterexamples in Optimal Control Theory written by Semen Ya. Serovaiskii and published by Walter de Gruyter. This book was released on 2011-12-01 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems by : Sergey I. Kabanikhin
Download or read book Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems written by Sergey I. Kabanikhin and published by Walter de Gruyter. This book was released on 2013-04-09 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Carleman Estimates for Coefficient Inverse Problems and Numerical Applications by : Michael V. Klibanov
Download or read book Carleman Estimates for Coefficient Inverse Problems and Numerical Applications written by Michael V. Klibanov and published by Walter de Gruyter. This book was released on 2012-04-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Inverse and Ill-posed Problems by : Heinz W. Engl
Download or read book Inverse and Ill-posed Problems written by Heinz W. Engl and published by . This book was released on 1987 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse and Ill-Posed Problems.
Book Synopsis Polyharmonic Boundary Value Problems by : Filippo Gazzola
Download or read book Polyharmonic Boundary Value Problems written by Filippo Gazzola and published by Springer Science & Business Media. This book was released on 2010-06-03 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.
Book Synopsis Nonclassical Linear Volterra Equations of the First Kind by : Anatoly S. Apartsyn
Download or read book Nonclassical Linear Volterra Equations of the First Kind written by Anatoly S. Apartsyn and published by Walter de Gruyter. This book was released on 2011-03-01 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with linear integra Volterra equations of the first kind with variable upper and lower limits of integration. Volterra operators of this type are the basic operators for integral models of dynamic systems.
Book Synopsis Inverse Problems of Mathematical Physics by : Mikhail M. Lavrent'ev
Download or read book Inverse Problems of Mathematical Physics written by Mikhail M. Lavrent'ev and published by Walter de Gruyter. This book was released on 2012-05-07 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Characterisation of Bio-Particles from Light Scattering by : Valeri P. Maltsev
Download or read book Characterisation of Bio-Particles from Light Scattering written by Valeri P. Maltsev and published by Walter de Gruyter. This book was released on 2013-03-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boundary Integral Equation Analysis of Singular, Potential, and Biharmonic Problems by : Derek B. Ingham
Download or read book Boundary Integral Equation Analysis of Singular, Potential, and Biharmonic Problems written by Derek B. Ingham and published by Springer. This book was released on 1984 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ill-Posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory by : Frederick Bloom
Download or read book Ill-Posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory written by Frederick Bloom and published by SIAM. This book was released on 1981-10-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines initial-history boundary-value problems associated with systems of partial-integrodifferential equations arising in mechanics and electromagnetic theories.
Book Synopsis Poorly Visible Media in X-Ray Tomography by : V. G. Nazarov
Download or read book Poorly Visible Media in X-Ray Tomography written by V. G. Nazarov and published by VSP. This book was released on 2002-01-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The tomography problem considered in this volume of the Inverse and Ill-Posed Problems Series consists of finding an essential part of information about the internal structure of an unknown medium. More particularly, the contact boundaries between various materials in the medium are sought. This investigation is implemented by studying an appropriate mathematical model, which is represented as a transport equation (linear Boltzmann's equation) together with certain boundary conditions. Both theoretical and numerical methods have been used and the results consist of proved theorems, computer testing of the corresponding algorithms, together with a number of tables. This book may be considered as a continuation and application of Transport Equation and Tomography by D.S. Anikonov, A.E. Kovtanyuk and I.V. Prokhorov, previously published in this series.
