Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation write by Mukarram A. Atakhodzhaev. This book was released on 2014-07-24. Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation available in PDF, EPUB and Kindle. 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.
Ill-Posed Boundary-Value Problems
Ill-Posed Boundary-Value Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ill-Posed Boundary-Value Problems write by Serikkali E. Temirbolat. This book was released on 2012-06-04. Ill-Posed Boundary-Value Problems available in PDF, EPUB and Kindle. 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.
Operator Theory and Ill-Posed Problems
Operator Theory and Ill-Posed Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Theory and Ill-Posed Problems write by Mikhail M. Lavrent'ev. This book was released on 2011-12-22. Operator Theory and Ill-Posed Problems available in PDF, EPUB and Kindle. 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.
Well-posed, Ill-posed, and Intermediate Problems with Applications
Well-posed, Ill-posed, and Intermediate Problems with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Well-posed, Ill-posed, and Intermediate Problems with Applications write by Petrov Yuri P.. This book was released on 2011-12-22. Well-posed, Ill-posed, and Intermediate Problems with Applications available in PDF, EPUB and Kindle. 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.
Theory of Linear Ill-Posed Problems and its Applications
Theory of Linear Ill-Posed Problems and its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory of Linear Ill-Posed Problems and its Applications write by Valentin K. Ivanov. This book was released on 2013-02-18. Theory of Linear Ill-Posed Problems and its Applications available in PDF, EPUB and Kindle. 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.
