Functional Analysis And Boundary Value Problems
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Functional Analysis And Boundary Value Problems
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Author : B. Dayanand Reddy
language : en
Publisher: Longman Scientific and Technical
Release Date : 1986
Functional Analysis And Boundary Value Problems written by B. Dayanand Reddy and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Introductory Functional Analysis
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Author : B.D. Reddy
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Introductory Functional Analysis written by B.D. Reddy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Providing an introduction to functional analysis, this text treats in detail its application to boundary-value problems and finite elements, and is distinguished by the fact that abstract concepts are motivated and illustrated wherever possible. It is intended for use by senior undergraduates and graduates in mathematics, the physical sciences and engineering, who may not have been exposed to the conventional prerequisites for a course in functional analysis, such as real analysis. Mature researchers wishing to learn the basic ideas of functional analysis will equally find this useful. Offers a good grounding in those aspects of functional analysis which are most relevant to a proper understanding and appreciation of the mathematical aspects of boundary-value problems and the finite element method.
The Moravian Lovefeast
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Author :
language : en
Publisher:
Release Date : 19??
The Moravian Lovefeast written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 19?? with Lovefeast, Moravian categories.
Singularly Perturbed Boundary Value Problems
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Author : Matteo Dalla Riva
language : en
Publisher: Springer Nature
Release Date : 2021-10-01
Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.
This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.
Green S Functions And Boundary Value Problems
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Author : Ivar Stakgold
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01
Green S Functions And Boundary Value Problems written by Ivar Stakgold and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
Praise for the Second Edition "This book is an excellent introduction to the wide field of boundary value problems."—Journal of Engineering Mathematics "No doubt this textbook will be useful for both students and research workers."—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.
Boundary Value Problems Weyl Functions And Differential Operators
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Author : Jussi Behrndt
language : en
Publisher: Springer Nature
Release Date : 2020-01-03
Boundary Value Problems Weyl Functions And Differential Operators written by Jussi Behrndt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
Boundary Value Problems And Markov Processes
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Author : Kazuaki Taira
language : en
Publisher: Springer Nature
Release Date : 2020-07-01
Boundary Value Problems And Markov Processes written by Kazuaki Taira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-01 with Mathematics categories.
This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject. The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.
Singularly Perturbed Boundary Value Problems
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Author : Luminita Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14
Singularly Perturbed Boundary Value Problems written by Luminita Barbu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Mathematics categories.
This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for phenomena in biology, chemistry, and engineering. The authors are particularly interested in nonlinear problems, which have gone little-examined so far in literature dedicated to singular perturbations. The treatment presented here combines successful results from functional analysis, singular perturbation theory, partial differential equations, and evolution equations.
Continual Means And Boundary Value Problems In Function Spaces
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Author : E. Polishchuk
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Continual Means And Boundary Value Problems In Function Spaces written by E. Polishchuk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The fates of important mathematical ideas are varied. Sometimes they are instantly appreciated by the specialists and constitute the foundation of the development of theories or methods. It also happens, however, that even ideas uttered by distinguished mathematicians are surrounded with respectful indifference for a long time, and every effort of inter preters and successors has to be made in order to gain for them the merit deserved. It is the second case that is encountered in the present book, the author of which, the Leningrad mathematician E.M. Polishchuk, reconstructs and develops one of the dir.ctions in functional analysis that originated from Hadamard and Gateaux and was newly thought over and taken as the basis of a prospective theory by Paul Levy. Paul Levy, Member of the French Academy of Sciences, whose centenary of his birthday was celebrated in 1986, was one of the most original mathe matiCians of the second half of the 20th century. He could not complain about a lack of attention to his ideas and results. Together with A.N. Kolmogorov, A.Ya. Khinchin and William Feller, he is indeed one of the acknowledged founders of the theory of random processes. In the proba bility theory and, to a lesser degree, in functional analysis his work is well-known for its conceptualization and scope of the problems posed.
Functional Analysis And Approximation Theory In Numerical Analysis
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Author : R. S. Varga
language : en
Publisher: SIAM
Release Date : 1971-01-01
Functional Analysis And Approximation Theory In Numerical Analysis written by R. S. Varga and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-01-01 with Mathematics categories.
Surveys the enormous literature on numerical approximation of solutions of elliptic boundary problems by means of variational and finite element methods, requiring almost constant application of results and techniques from functional analysis and approximation theory to the field of numerical analysis.