Integro Differential Operators

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Inverse Problems For Integro Differential Operators

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Author : Yi-Hsuan Lin
language : en
Publisher: Springer Nature
Release Date :

Inverse Problems For Integro Differential Operators written by Yi-Hsuan Lin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Topics In Integral And Integro Differential Equations

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Author : Harendra Singh
language : en
Publisher: Springer Nature
Release Date : 2021-03-15

Topics In Integral And Integro Differential Equations written by Harendra Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-15 with Technology & Engineering categories.

This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations

Integro Differential Elliptic Equations

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Author : Xavier Fernández-Real
language : en
Publisher: Springer Nature
Release Date : 2024-04-24

Integro Differential Elliptic Equations written by Xavier Fernández-Real and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.

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.

Integral And Integrodifferential Equations

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Author : Ravi P. Agarwal
language : en
Publisher: CRC Press
Release Date : 2000-03-09

Integral And Integrodifferential Equations written by Ravi P. Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-09 with Mathematics categories.

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.

Partial Integral Operators And Integro Differential Equations

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Author : Jurgen Appell
language : en
Publisher: CRC Press
Release Date : 2000-02-29

Partial Integral Operators And Integro Differential Equations written by Jurgen Appell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-29 with Mathematics categories.

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 linea

Linear And Nonlinear Integral Equations

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Author : Abdul-Majid Wazwaz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-24

Linear And Nonlinear Integral Equations written by Abdul-Majid Wazwaz 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 2011-11-24 with Mathematics categories.

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.

Existence Theory For Nonlinear Integral And Integrodifferential Equations

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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Existence Theory For Nonlinear Integral And Integrodifferential Equations written by Donal O'Regan 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.

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.

Integro Differential Operators

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Author : Reshma Menon
language : en
Publisher:
Release Date : 2020

Integro Differential Operators written by Reshma Menon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic dissertations categories.

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.

Theory Of Integro Differential Equations

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Author : V. Lakshmikantham
language : en
Publisher: CRC Press
Release Date : 1995-03-15

Theory Of Integro Differential Equations written by V. Lakshmikantham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-15 with Mathematics categories.

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.

Finite Element Methods For Integrodifferential Equations

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Author : Chuan Miao Chen
language : en
Publisher: World Scientific
Release Date : 1998-02-28

Finite Element Methods For Integrodifferential Equations written by Chuan Miao Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-28 with Mathematics categories.

Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations possess new physical and mathematical properties. This monograph systematically discusses application of the finite element methods to numerical solution of integrodifferential equations. It will be useful for numerical analysts, mathematicians, physicists and engineers. Advanced undergraduates and graduate students should also find it beneficial.