A Concise Guide To Semigroups And Evolution Equations

A Concise Guide To Semigroups And Evolution Equations

Author: Belleni-morante Aldo

Publisher: World Scientific

Published: 1994-05-18

Total Pages: 180

ISBN-13: 9813104570

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This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).


Book Synopsis A Concise Guide To Semigroups And Evolution Equations by : Belleni-morante Aldo

Download or read book A Concise Guide To Semigroups And Evolution Equations written by Belleni-morante Aldo and published by World Scientific. This book was released on 1994-05-18 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).

A Concise Guide to Semigroups and Evolution Equations

A Concise Guide to Semigroups and Evolution Equations

Author: Aldo Belleni-Morante

Publisher: World Scientific

Published: 1994

Total Pages: 188

ISBN-13: 9789810212940

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This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).


Book Synopsis A Concise Guide to Semigroups and Evolution Equations by : Aldo Belleni-Morante

Download or read book A Concise Guide to Semigroups and Evolution Equations written by Aldo Belleni-Morante and published by World Scientific. This book was released on 1994 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).

Discovering Evolution Equations with Applications

Discovering Evolution Equations with Applications

Author: Mark McKibben

Publisher: CRC Press

Published: 2010-07-19

Total Pages: 458

ISBN-13: 1420092073

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Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging, accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. It gives nonspecialists, even those with minimal prior exposure to analysis, the foundation to understand what evolution equations are and how to work with them in various areas of practice. After presenting the essentials of analysis, the book discusses homogenous finite-dimensional ordinary differential equations. Subsequent chapters then focus on linear homogenous abstract, nonhomogenous linear, semi-linear, functional, Sobolev-type, neutral, delay, and nonlinear evolution equations. The final two chapters explore research topics, including nonlocal evolution equations. For each class of equations, the author develops a core of theoretical results concerning the existence and uniqueness of solutions under various growth and compactness assumptions, continuous dependence upon initial data and parameters, convergence results regarding the initial data, and elementary stability results. By taking an applications-oriented approach, this self-contained, conversational-style book motivates readers to fully grasp the mathematical details of studying evolution equations. It prepares newcomers to successfully navigate further research in the field.


Book Synopsis Discovering Evolution Equations with Applications by : Mark McKibben

Download or read book Discovering Evolution Equations with Applications written by Mark McKibben and published by CRC Press. This book was released on 2010-07-19 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging, accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. It gives nonspecialists, even those with minimal prior exposure to analysis, the foundation to understand what evolution equations are and how to work with them in various areas of practice. After presenting the essentials of analysis, the book discusses homogenous finite-dimensional ordinary differential equations. Subsequent chapters then focus on linear homogenous abstract, nonhomogenous linear, semi-linear, functional, Sobolev-type, neutral, delay, and nonlinear evolution equations. The final two chapters explore research topics, including nonlocal evolution equations. For each class of equations, the author develops a core of theoretical results concerning the existence and uniqueness of solutions under various growth and compactness assumptions, continuous dependence upon initial data and parameters, convergence results regarding the initial data, and elementary stability results. By taking an applications-oriented approach, this self-contained, conversational-style book motivates readers to fully grasp the mathematical details of studying evolution equations. It prepares newcomers to successfully navigate further research in the field.

Evolution Equations and Approximations

Evolution Equations and Approximations

Author: Kazufumi Ito

Publisher: World Scientific

Published: 2002

Total Pages: 524

ISBN-13: 9789812380265

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Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR


Book Synopsis Evolution Equations and Approximations by : Kazufumi Ito

Download or read book Evolution Equations and Approximations written by Kazufumi Ito and published by World Scientific. This book was released on 2002 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR

Singularly Perturbed Evolution Equations with Applications to Kinetic Theory

Singularly Perturbed Evolution Equations with Applications to Kinetic Theory

Author: J. R. Mika

Publisher: World Scientific

Published: 1995

Total Pages: 332

ISBN-13: 9789810221256

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In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.


Book Synopsis Singularly Perturbed Evolution Equations with Applications to Kinetic Theory by : J. R. Mika

Download or read book Singularly Perturbed Evolution Equations with Applications to Kinetic Theory written by J. R. Mika and published by World Scientific. This book was released on 1995 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.

Qualitative Estimates For Partial Differential Equations

Qualitative Estimates For Partial Differential Equations

Author: J N Flavin

Publisher: CRC Press

Published: 2020-12-17

Total Pages: 389

ISBN-13: 1000099350

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Qualitative Estimates For Partial Differential Equations: An Introduction describes an approach to the use of partial differential equations (PDEs) arising in the modelling of physical phenomena. It treats a wide range of differential inequality techniques applicable to problems arising in engineering and the natural sciences, including fluid and solid mechanics, physics, dynamics, biology, and chemistry. The book begins with an elementary discussion of the fundamental principles of differential inequality techniques for PDEs arising in the solution of physical problems, and then shows how these are used in research. Qualitative Estimates For Partial Differential Equations: An Introduction is an ideal book for students, professors, lecturers, and researchers who need a comprehensive introduction to qualitative methods for PDEs arising in engineering and the natural sciences.


Book Synopsis Qualitative Estimates For Partial Differential Equations by : J N Flavin

Download or read book Qualitative Estimates For Partial Differential Equations written by J N Flavin and published by CRC Press. This book was released on 2020-12-17 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Qualitative Estimates For Partial Differential Equations: An Introduction describes an approach to the use of partial differential equations (PDEs) arising in the modelling of physical phenomena. It treats a wide range of differential inequality techniques applicable to problems arising in engineering and the natural sciences, including fluid and solid mechanics, physics, dynamics, biology, and chemistry. The book begins with an elementary discussion of the fundamental principles of differential inequality techniques for PDEs arising in the solution of physical problems, and then shows how these are used in research. Qualitative Estimates For Partial Differential Equations: An Introduction is an ideal book for students, professors, lecturers, and researchers who need a comprehensive introduction to qualitative methods for PDEs arising in engineering and the natural sciences.

Feedback Control Theory for Dynamic Traffic Assignment

Feedback Control Theory for Dynamic Traffic Assignment

Author: Pushkin Kachroo

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 219

ISBN-13: 1447108159

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The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology impacts all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies, .... , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. Micro-technology and modern communications technology are revolutionising many aspects of our daily lives and so it is not surprising that it is impacting societal transportation systems whether our highways, airways, seaways or railways. The Advances in Industrial Control series reported on these developments for long haul railway systems in a monograph by Howlett and Pudney (ISBN 3-S40-19990-X, 1995). Now it is the turn of transportation in a contribution from Pushkin Kachroo and Kaan Ozbay. The authors viewpoint is that this new set of transportation problems are control problems and that control engineers should be highly active in this field. Their volume covers all the aspects of modelling, problem formulation, and applies various control methodologies to solve the control problems formulated.


Book Synopsis Feedback Control Theory for Dynamic Traffic Assignment by : Pushkin Kachroo

Download or read book Feedback Control Theory for Dynamic Traffic Assignment written by Pushkin Kachroo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology impacts all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies, .... , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. Micro-technology and modern communications technology are revolutionising many aspects of our daily lives and so it is not surprising that it is impacting societal transportation systems whether our highways, airways, seaways or railways. The Advances in Industrial Control series reported on these developments for long haul railway systems in a monograph by Howlett and Pudney (ISBN 3-S40-19990-X, 1995). Now it is the turn of transportation in a contribution from Pushkin Kachroo and Kaan Ozbay. The authors viewpoint is that this new set of transportation problems are control problems and that control engineers should be highly active in this field. Their volume covers all the aspects of modelling, problem formulation, and applies various control methodologies to solve the control problems formulated.

Multigroup Equations for the Description of the Particle Transport in Semiconductors

Multigroup Equations for the Description of the Particle Transport in Semiconductors

Author: Martin Galler

Publisher: World Scientific

Published: 2005

Total Pages: 247

ISBN-13: 9812563555

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Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail.This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.


Book Synopsis Multigroup Equations for the Description of the Particle Transport in Semiconductors by : Martin Galler

Download or read book Multigroup Equations for the Description of the Particle Transport in Semiconductors written by Martin Galler and published by World Scientific. This book was released on 2005 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deterministic simulation of the particle transport in semiconductor devices is an interesting alternative to the common Monte Carlo approach. In this book, a state-of-the-art technique called the multigroup approach is presented and applied to a variety of transport problems in bulk semiconductors and semiconductor devices. High-field effects as well as hot-phonon phenomena in polar semiconductors are studied in detail. The mathematical properties of the presented numerical method are studied, and the method is applied to simulating the transport of a two-dimensional electron gas formed at a semiconductor heterostructure. Concerning semiconductor device simulation, several diodes and transistors fabricated of silicon and gallium arsenide are investigated. For all of these simulations, the numerical techniques employed are discussed in detail.This unique study of the application of direct methods for semiconductor device simulation provides the interested reader with an indispensable reference on this growing research area.

Impulsive Differential Equations with a Small Parameter

Impulsive Differential Equations with a Small Parameter

Author: Dimit?r Ba?nov

Publisher: World Scientific

Published: 1994

Total Pages: 292

ISBN-13: 9789810214340

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This book is devoted to impulsive differential equations with a small parameter. It consists of three chapters. Chapter One serves as an introduction. In Chapter Two, regularly perturbed impulsive differential equations are considered. Modifications of the method of small parameter, the averaging method, and the method of integral manifolds are proposed. In Chapter Three, singularly perturbed differential equations are considered. A modification of the method of boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated, such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method.The book is written clearly, strictly, and understandably. It is intended for mathematicians, physicists, chemists, biologists and economists, as well as for senior students of these specialities.


Book Synopsis Impulsive Differential Equations with a Small Parameter by : Dimit?r Ba?nov

Download or read book Impulsive Differential Equations with a Small Parameter written by Dimit?r Ba?nov and published by World Scientific. This book was released on 1994 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to impulsive differential equations with a small parameter. It consists of three chapters. Chapter One serves as an introduction. In Chapter Two, regularly perturbed impulsive differential equations are considered. Modifications of the method of small parameter, the averaging method, and the method of integral manifolds are proposed. In Chapter Three, singularly perturbed differential equations are considered. A modification of the method of boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated, such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method.The book is written clearly, strictly, and understandably. It is intended for mathematicians, physicists, chemists, biologists and economists, as well as for senior students of these specialities.

Impulsive Differential Equations: Asymptotic Properties Of The Solutions

Impulsive Differential Equations: Asymptotic Properties Of The Solutions

Author: Drumi D Bainov

Publisher: World Scientific

Published: 1995-03-29

Total Pages: 246

ISBN-13: 9814501883

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The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.


Book Synopsis Impulsive Differential Equations: Asymptotic Properties Of The Solutions by : Drumi D Bainov

Download or read book Impulsive Differential Equations: Asymptotic Properties Of The Solutions written by Drumi D Bainov and published by World Scientific. This book was released on 1995-03-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.