Differential Operator Equations
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Fundamental Solutions For Differential Operators And Applications
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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-07-30
Fundamental Solutions For Differential Operators And Applications written by Prem Kythe 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 1996-07-30 with Mathematics categories.
A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.
Pseudo Differential Operators Complex Analysis And Partial Differential Equations
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Author : Bert-Wolfgang Schulze
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-01
Pseudo Differential Operators Complex Analysis And Partial Differential Equations written by Bert-Wolfgang Schulze 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 2010-03-01 with Mathematics categories.
Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.
Differential Operator Equations
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Author : Yakov Yakubov
language : en
Publisher: CRC Press
Release Date : 1999-11-24
Differential Operator Equations written by Yakov Yakubov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-24 with Mathematics categories.
The theory of differential-operator equations is one of two modern theories for the study of both ordinary and partial differential equations, with numerous applications in mechanics and theoretical physics. Although a number of published works address differential-operator equations of the first and second orders, to date none offer a treatment of the higher orders. In Differential-Operator Equations, the authors present a systematic treatment of the theory of differential-operator equations of higher order, with applications to partial differential equations. They construct a theory that allows application to both regular and irregular differential problems. In particular, they study problems that cannot be solved by various known methods and irregular problems not addressed in existing monographs. These include Birkhoff-irregularity, non-local boundary value conditions, and non-smoothness of the boundary of the domains. Among this volume's other points of interest are: The Abel basis property of a system of root functions Irregular boundary value problems The theory of hyperbolic equations in Gevrey space The theory of boundary value problems for elliptic differential equations with a parameter
Introduction To Pseudo Differential Operators An 3rd Edition
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Author : Man-wah Wong
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-03-11
Introduction To Pseudo Differential Operators An 3rd Edition written by Man-wah Wong and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-11 with Mathematics categories.
The aim of this third edition is to give an accessible and essentially self-contained account of pseudo-differential operators based on the previous edition. New chapters notwithstanding, the elementary and detailed style of earlier editions is maintained in order to appeal to the largest possible group of readers. The focus of this book is on the global theory of elliptic pseudo-differential operators on Lp(Rn).The main prerequisite for a complete understanding of the book is a basic course in functional analysis up to the level of compact operators. It is an ideal introduction for graduate students in mathematics and mathematicians who aspire to do research in pseudo-differential operators and related topics.
Homogenization Of Differential Operators And Integral Functionals
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Author : V.V. Jikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homogenization Of Differential Operators And Integral Functionals written by V.V. Jikov 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 2012-12-06 with Mathematics categories.
It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.
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.
Linear Operator Equations Approximation And Regularization
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Author : M Thamban Nair
language : en
Publisher: World Scientific
Release Date : 2009-05-05
Linear Operator Equations Approximation And Regularization written by M Thamban Nair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-05 with Mathematics categories.
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
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.
The Analysis Of Linear Partial Differential Operators I
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Author : Lars Hörmander
language : en
Publisher: Springer
Release Date : 1990-08-10
The Analysis Of Linear Partial Differential Operators I written by Lars Hörmander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-10 with Mathematics categories.
The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.
Spectral Analysis Of Differential Operators
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Author : Fedor S. Rofe-Beketov
language : en
Publisher: World Scientific
Release Date : 2005
Spectral Analysis Of Differential Operators written by Fedor S. Rofe-Beketov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
- Detailed bibliographical comments and some open questions are given after each chapter - Indicates connections between the content of the book and many other topics in mathematics and physics - Open questions are formulated and commented with the intention to attract attention of young mathematicians