Theory and Applications of Partial Functional Differential Equations
Theory and Applications of Partial Functional Differential Equations

Author: Jianhong Wu

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 441

ISBN-13: 1461240506

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Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

Nonoscillation Theory of Functional Differential Equations with Applications
Nonoscillation Theory of Functional Differential Equations with Applications

Author: Ravi P. Agarwal

Publisher: Springer Science & Business Media

Published: 2012-04-23

Total Pages: 526

ISBN-13: 1461434556

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This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.​

Applied Theory of Functional Differential Equations
Applied Theory of Functional Differential Equations

Author: V. Kolmanovskii

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 246

ISBN-13: 9401580847

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This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

Theory and applications of partial functional differential equations
Theory and applications of partial functional differential equations

Author: Amanora Puniest

Publisher:

Published:

Total Pages: 238

ISBN-13: 9781680952490

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A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Abstract semi linear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this textis to provide an introduction of the qualitative theory and applications of differential equations. The book "Theory and Applications of Partial Fucntional Differential Equations" contains ten chapters. The similarity reduction of poplinear partial differential equations has been discussed in first chapter. In second chapter, we propose new results in quadruple Laplace transform and prove some properties concerned with quadruple Laplace transform. The purpose of third chapter is to investigate global asymptotic stability of the zero solution of the fifth-order nonlinear delay differential equation. The modified simple equation method has been extended in fourth chapter to get the exact solutions of nonlinear partial time-space differential equations of fractional order. In fifth chapter, the VIM method is used to solve the quadratic optimal control problem of systems governed by linear PDEs. A partial information non-zero sum differential game of backward stochastic differential equations with applications has been introduced in sixth chapter. The aim of seventh chapter is to prove a few Leggert-Williams type theorems, in particular for a more general class of mappings than compact ones. Eighth chapter presents an experiment of improving the performance of spectral stochastic finite element method using high-order elements. We establish sufficient conditions for the existence of solutions for some partial functional differential equations to actual program has been proposed in last chapter.

Bifurcation Theory of Functional Differential Equations
Bifurcation Theory of Functional Differential Equations

Author: Shangjiang Guo

Publisher: Springer Science & Business Media

Published: 2013-07-30

Total Pages: 295

ISBN-13: 1461469929

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This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

Elliptic Functional Differential Equations and Applications
Elliptic Functional Differential Equations and Applications

Author: Alexander L. Skubachevskii

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 298

ISBN-13: 3034890338

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Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved only in some subdomains. The symbol of a self-adjoint semibounded functional differential operator can change its sign. The purpose of this book is to present for the first time general results concerning solvability and spectrum of these problems, a priori estimates and smoothness of solutions. The approach is based on the properties of elliptic operators and difference operators in Sobolev spaces. The most important features distinguishing this work are applications to different fields of science. The methods in this book are used to obtain new results regarding the solvability of nonlocal elliptic boundary value problems and the existence of Feller semigroups for multidimensional diffusion processes. Moreover, applications to control theory and aircraft and rocket technology are given. The theory is illustrated with numerous figures and examples. The book is addresssed to graduate students and researchers in partial differential equations and functional differential equations. It will also be of use to engineers in control theory and elasticity theory.

Theory and Applications of Partial Differential Equations
Theory and Applications of Partial Differential Equations

Author: Piero Bassanini

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 446

ISBN-13: 1489918752

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This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

Delay and Functional Differential Equations and Their Applications
Delay and Functional Differential Equations and Their Applications

Author: Klaus Schmitt

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 414

ISBN-13: 1483272338

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Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.

Partial Differential Equations
Partial Differential Equations

Author: Michael Shearer

Publisher: Princeton University Press

Published: 2015-03-01

Total Pages: 286

ISBN-13: 0691161291

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An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors