Infinite Dimensional Dynamical Systems In Mechanics And Physics
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Infinite Dimensional Dynamical Systems In Mechanics And Physics
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Author : Roger Temam
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-04-01
Infinite Dimensional Dynamical Systems In Mechanics And Physics written by Roger Temam 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 1997-04-01 with Mathematics categories.
In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Hamiltonian Dynamical Systems And Applications
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Author : Walter Craig
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Hamiltonian Dynamical Systems And Applications written by Walter Craig 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 2008-02-17 with Mathematics categories.
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Infinite Dimensional Dynamical Systems
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Author : James C. Robinson
language : en
Publisher: Cambridge University Press
Release Date : 2001-04-23
Infinite Dimensional Dynamical Systems written by James C. Robinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-23 with Mathematics categories.
This book develops the theory of global attractors for a class of parabolic PDEs that includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systemss of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves "finite-dimensional." The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.
Spinors And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry
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Author : Roger Penrose
language : en
Publisher: Cambridge University Press
Release Date : 1984
Spinors And Space Time Volume 2 Spinor And Twistor Methods In Space Time Geometry written by Roger Penrose and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
In the two volumes that comprise this work Roger Penrose and Wolfgang Rindler introduce the calculus of 2-spinors and the theory of twistors, and discuss in detail how these powerful and elegant methods may be used to elucidate the structure and properties of space-time. In volume 1, Two-spinor calculus and relativistic fields, the calculus of 2-spinors is introduced and developed. Volume 2, Spinor and twistor methods in space-time geometry, introduces the theory of twistors, and studies in detail how the theory of twistors and 2-spinors can be applied to the study of space-time. This work will be of great value to all those studying relativity, differential geometry, particle physics and quantum field theory from beginning graduate students to experts in these fields.
The Geometry Of Infinite Dimensional Groups
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Author : Boris Khesin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-28
The Geometry Of Infinite Dimensional Groups written by Boris Khesin 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 2008-09-28 with Mathematics categories.
This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.
Nonlinear Dynamics
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Author : Marc R Roussel
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2019-05-01
Nonlinear Dynamics written by Marc R Roussel and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-01 with Science categories.
This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.
Applied Functional Analysis
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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Functional Analysis written by Eberhard Zeidler 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.
A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question as quickly as possible. Here, one walks directly on the main road and does not wander into all the nice and interesting side roads. The present book is based on the second approach. It is addressed to undergraduate and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems that are related to our real world and that have played an important role in the history of mathematics. The reader should sense that the theory is being developed, not simply for its own sake, but for the effective solution of concrete problems. viii Preface Our introduction to applied functional analysis is divided into two parts: Part I: Applications to Mathematical Physics (AMS Vol. 108); Part II: Main Principles and Their Applications (AMS Vol. 109). A detailed discussion of the contents can be found in the preface to AMS Vol. 108.
Contemporary Approaches And Methods In Fundamental Mathematics And Mechanics
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Author : Victor A. Sadovnichiy
language : en
Publisher: Springer Nature
Release Date : 2020-11-24
Contemporary Approaches And Methods In Fundamental Mathematics And Mechanics written by Victor A. Sadovnichiy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-24 with Mathematics categories.
This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields
Partial Differential Equations And Functional Analysis
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Author : Andrew Comech
language : en
Publisher: Springer Nature
Release Date : 2023-10-14
Partial Differential Equations And Functional Analysis written by Andrew Comech and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-14 with Mathematics categories.
Mark Vishik was one of the prominent figures in the theory of partial differential equations. His ground-breaking contributions were instrumental in integrating the methods of functional analysis into this theory. The book is based on the memoirs of his friends and students, as well as on the recollections of Mark Vishik himself, and contains a detailed description of his biography: childhood in Lwów, his connections with the famous Lwów school of Stefan Banach, a difficult several year long journey from Lwów to Tbilisi after the Nazi assault in June 1941, going to Moscow and forming his own school of differential equations, whose central role was played by the famous Vishik Seminar at the Department of Mechanics and Mathematics at Moscow State University. The reader is introduced to a number of remarkable scientists whose lives intersected with Vishik’s, including S. Banach, J. Schauder, I. N. Vekua, N. I. Muskhelishvili, L. A. Lyusternik, I. G. Petrovskii, S. L. Sobolev, I. M. Gelfand, M. G. Krein, A. N. Kolmogorov, N. I. Akhiezer, J. Leray, J.-L. Lions, L. Schwartz, L. Nirenberg, and many others. The book also provides a detailed description of the main research directions of Mark Vishik written by his students and colleagues, as well as several reviews of the recent development in these directions.
Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory
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Author : Palle Jorgensen
language : en
Publisher: World Scientific
Release Date : 2021-01-15
Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory written by Palle Jorgensen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-15 with Mathematics categories.
The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.