Partial Differential Equations And Group Theory

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Partial Differential Equations And Group Theory

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Author : J.F. Pommaret
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Partial Differential Equations And Group Theory written by J.F. Pommaret 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 2013-03-09 with Mathematics categories.

Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.

Group Analysis Of Differential Equations

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Author : L. V. Ovsiannikov
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Group Analysis Of Differential Equations written by L. V. Ovsiannikov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.

Partial Differential Equations And Group Theory

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Author : J. F. Pommaret
language : en
Publisher:
Release Date : 2014-01-15

Partial Differential Equations And Group Theory written by J. F. Pommaret and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Advanced Course On Partial Differential Equations And Group Theory

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Author : Advanced Course on Partial Differential Equations and Group Theory (1992, Bonn)
language : en
Publisher:
Release Date : 1992

Advanced Course On Partial Differential Equations And Group Theory written by Advanced Course on Partial Differential Equations and Group Theory (1992, Bonn) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.

Group Theoretic Methods In Mechanics And Applied Mathematics

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Author : D.M. Klimov
language : en
Publisher: CRC Press
Release Date : 2014-04-21

Group Theoretic Methods In Mechanics And Applied Mathematics written by D.M. Klimov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-21 with Mathematics categories.

Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. Group-Theoretic Methods in Mechanics and Applied Mathematics systematizes the group analysis of the main postulates of classical and relativistic mechanics. Exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi, and more. The author pays particular attention to the application of group analysis to developing asymptotic methods for problems with small parameters. This book is designed for a broad audience of scientists, engineers, and students in the fields of applied mathematics, mechanics and physics.

Symmetries Of Partial Differential Equations

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Author : A.M. Vinogradov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Symmetries Of Partial Differential Equations written by A.M. Vinogradov 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.

2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) Abstract. The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. AMS subject classifications (1980). 35A30, 58005, 58035, 58H05. Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations. Also, some general views and perspectives will be discussed.

Group Theoretic Methods In Bifurcation Theory

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Author : David H. Sattinger
language : en
Publisher: Springer
Release Date : 2006-11-15

Group Theoretic Methods In Bifurcation Theory written by David H. Sattinger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Ischemia and Loss of Vascular Autoregulation in Ocular and Cerebral Diseases: A New Perspective presents evidence that ischemia and loss of autoregulation of blood flow are associated with the onset of the major ocular and cerebral diseases including macular degeneration, diabetic retinopathy, low and normal tension open angle glaucoma, stroke and Alzheimer's disease. Recognition of these vascular changes underline the critical need for clinicians to monitor blood flow and autoregulation to improve early diagnosis and to optimize therapies of ocular and cerebral vascular diseases. The text brings to clinicians in Ophthalmology, Neurology, Medicine, Optometry and Geriatrics decisive guidance on the practical aspects for early diagnosis and treatment of ocular and cerebral diseases. The author brings together in a concise form the progress made over the span of his career and provides new perspectives and understanding of the fluid circulations of the eye and the brain. In addition, he explains the new analytical technologies that made the new concepts possible. The physiological and functional importance of blood flow autoregulation in the eye and in the brain in minimizing the progression of pathology, including the ischemia resulting from stenosis of the internal carotid artery and stroke, are also presented . ABOUT THE AUTHOR: Dr. Langham was born in London, England. In 1947, he joined the Ophthalmological Research Unit, newly formed by the Medical Research Council of the United Kingdom under the direction of Sir Stewart Duke-Elder. In 1956, the author enjoyed a research fellowship at Harvard University. After returning to England for a time, he accepted a position of Associate Professor of Ophthalmology and Director of Research at the Wilmer Ophthalmological Institute of the Johns Hopkins Hospital and Medical school in 1959. There he initiated a program in which all residents spent time engaged in research. This productive interaction between the disciplines led to many important clinical diagnostic and therapeutic advances.

Quantized Partial Differential Equations

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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 2004

Quantized Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This book presents, for the first time, a systematic formulation of the geometric theory of noncommutative PDE's which is suitable enough to be used for a mathematical description of quantum dynamics and quantum field theory. A geometric theory of supersymmetric quantum PDE's is also considered, in order to describe quantum supergravity. Covariant and canonical quantizations of (super) PDE's are shown to be founded on the geometric theory of PDE's and to produce quantum (super) PDE's by means of functors from the category of commutative (super) PDE's to the category of quantum (super) PDE's. Global properties of solutions to (super) (commutative) PDE's are obtained by means of their integral bordism groups.

Geometrical Properties Of Differential Equations Applications Of The Lie Group Analysis In Financial Mathematics

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Author : Ljudmila A Bordag
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-05-27

Geometrical Properties Of Differential Equations Applications Of The Lie Group Analysis In Financial Mathematics written by Ljudmila A Bordag 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 2015-05-27 with Mathematics categories.

This textbook is a short comprehensive and intuitive introduction to Lie group analysis of ordinary and partial differential equations. This practical-oriented material contains a large number of examples and problems accompanied by detailed solutions and figures. In comparison with the known beginner guides to Lie group analysis, the book is oriented toward students who are interested in financial mathematics, mathematical finance and economics.We provide the results of the Lie group analysis of actual models in Financial Mathematics using recent publications. These models are usually formulated as nonlinear partial differential equations and are rather difficult to make use of. With the help of Lie group analysis it is possible to describe some important properties of these models and to obtain interesting reductions in a clear and understandable algorithmic way.The book can serve as a short introduction for a further study of modern geometrical analysis applied to models in financial mathematics. It can also be used as textbook in a master's program, in an intensive compact course, or for self study.The textbook with a large number of examples will be useful not only for students who are interested in Financial Mathematics but also for people who are working in other areas of research that are not directly connected with Physics (for instance in such areas of Applied Mathematics like mathematical economy, bio systems, coding theory, etc.).

Emergence Of The Theory Of Lie Groups

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Author : Thomas Hawkins
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Emergence Of The Theory Of Lie Groups written by Thomas Hawkins 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.

This book is both more and less than a history of the theory of Lie groups during the period 1869-1926. No attempt has been made to provide an exhaustive treatment of all aspects of the theory. Instead, I have focused upon its origins and upon the subsequent development of its structural as pects, particularly the structure and representation of semisimple groups. In dealing with this more limited subject matter, considerable emphasis has been placed upon the motivation behind the mathematics. This has meant paying close attention to the historical context: the mathematical or physical considerations that motivate or inform the work of a particular mathematician as well as the disciplinary ideals of a mathematical school that encourage research in certain directions. As a result, readers will ob tain in the ensuing pages glimpses of and, I hope, the flavor of many areas of nineteenth and early twentieth century geometry, algebra, and analysis. They will also encounter many of the mathematicians of the period, includ ing quite a few not directly connected with Lie groups, and will become acquainted with some of the major mathematical schools. In this sense, the book is more than a history of the theory of Lie groups. It provides a different perspective on the history of mathematics between, roughly, 1869 and 1926. Hence the subtitle.