Download or read book An Integro differential Operator written by Edward A. Catchpole and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Integral Operators and Integro Differential Equations written by Jurgen Appell and published by CRC Press. This book was released on 2000-02-29 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.
Download or read book Theory of Integro Differential Equations written by V. Lakshmikantham and published by CRC Press. This book was released on 1995-03-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.
Download or read book Integro differential Operators written by Reshma Menon and published by . This book was released on 2020 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study aspects of integro-differential operators, and how they relate to different types of equations. In each case, we use information and results about the operators in a lower dimension to analyse an equation in a higher dimension, and vice-versa. We begin in chapter 1 with an introduction to the operators and equations we will be considering.In Chapters 2 and 3, we discuss certain integro-differential operators of functions in a relatively smooth space. However, to understand more about the structure of these operators, particularly about the measure associated with them, we study certain equations in a higher dimension such as degenerate elliptic equations in the upper half space. We analyse the solution of such an equation and its gradient, followed by estimates on its Green's function and Poisson kernel. These estimates then help reveal some properties of the measure associated with the integro-differential operator in the lower dimension. The structure of the degenerate elliptic equations is similar to that of uniformly elliptic equations, but with an additional complexity of a term which involves distance to the boundary. This degeneracy complicates the analysis; as such, the classical techniques of finding pointwise estimates as mentioned above do not work so well anymore. So we provide some revised results for the same. Thus understanding an equation in a higher dimension gives us information about an integro-differential operator in a lower dimension.In Chapters 4 and 5, we prove some results about the solutions of free boundary problems in Rn+1 x [0, T], where the free boundary for a fixed time t can be seen as the graph of a function over a sphere. This time, we connect the solution of the free boundary problem to the solution of a parabolic equation on the sphere - that is, in a lower dimension. This parabolic equation involves an integro-differential operator, which has a min-max representation that is consistent with all the results about viscosity solutions of parabolic equations in Rn. We modify these results for parabolic equations on the sphere, which then gives us existence and uniqueness results about the free boundary problem in a higher dimension.
Download or read book Peridynamic Differential Operator for Numerical Analysis written by Erdogan Madenci and published by Springer. This book was released on 2019-01-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data. This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization. Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.
Download or read book Second Order Elliptic Integro Differential Problems written by Maria Giovanna Garroni and published by CRC Press. This book was released on 2002-02-20 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Green function has played a key role in the analytical approach that in recent years has led to important developments in the study of stochastic processes with jumps. In this Research Note, the authors-both regarded as leading experts in the field- collect several useful results derived from the construction of the Green function and its estim
Download or read book Existence Theory for Nonlinear Integral and Integrodifferential Equations written by Donal O'Regan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in tegral inclusions, stochastic equations and periodic problems. We note that the selected topics reflect the particular interests of the authors. Donal 0 'Regan Maria Meehan CHAPTER 1 INTRODUCTION AND PRELIMINARIES 1.1. Introduction The aim of this book is firstly to provide a comprehensive existence the ory for integral and integrodifferential equations, and secondly to present some specialised topics in integral equations which we hope will inspire fur ther research in the area. To this end, the first part of the book deals with existence principles and results for nonlinear, Fredholm and Volterra inte gral and integrodifferential equations on compact and half-open intervals, while selected topics (which reflect the particular interests of the authors) such as nonresonance and resonance problems, equations in Banach spaces, inclusions, and stochastic equations are presented in the latter part.
Download or read book Some Identification Problems for Integro differential Operator Equations written by A. Lorenzi and published by . This book was released on 2000 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear and Nonlinear Integral Equations written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.
Download or read book Linear Differential Operators written by Cornelius Lanczos and published by SIAM. This book was released on 1997-12-01 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field."
Download or read book Integral and Integrodifferential Equations written by Ravi P. Agarwal and published by CRC Press. This book was released on 2000-03-09 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.
Download or read book Intertwining Operators Associated with a Singular Integro Differential Operator on the Real Line and Certain of Their Applications International Journal of Open Problems in Complex Analysis 2013 Vol 5 No 3 written by Mohamed Ali Mourou and published by . This book was released on 2013 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Direct and Inverse Problems for Second order Integro differential Operator Equations in an Unbounded Time Interval written by Alfredo Lorenzi and published by . This book was released on 2001 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fundamental Solutions for Differential Operators and Applications written by Prem Kythe and published by Springer Science & Business Media. This book was released on 1996-07-30 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Recovering a Leading Coefficient and a Memory Kernel in First order Integro differential Operator Equations written by Alberto Favaron and published by . This book was released on 2001 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integro Differential Elliptic Equations written by Xavier Fernández-Real and published by Springer Nature. This book was released on 2024 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters
Download or read book Direct and Inverse Problems for Second order Integro differential Operator Equations Subject to Non initial Conditions written by Alfredo Lorenzi and published by . This book was released on 2002 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
