Dynamics Of Infinite Dimensional Systems

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Dynamics of Infinite Dimensional Systems

Author : Shui-Nee Chow,Jack K. Hale
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 42,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783642864582

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Dynamics of Infinite Dimensional Systems by Shui-Nee Chow,Jack K. Hale Pdf

The 1986 NATO Advanced Study Insti tute on Dynamics of Infini te Dimensional Systems was held at the Instituto Superior Tecnico. Lisbon. Portugal. In recent years. there have been several research workers who have been considering partial differential equations and functional differential equations as dynamical systems on function spaces. Such approaches have led to the formulation of more theoretical problems that need to be investigated. In the applications. the theoretical ideas have contributed significantly to a better understanding of phenomena that have been experimentally and computationally observed. The investigators of this development come wi th several different backgrounds - some from classical partial differential equations. some from classical ordinary differential equations and some interested in specific applications. Each group has special ideas and often these ideas have not been transmitted from one group to another. The purpose of this NATO Workshop was to bring together research workers from these various areas. It provided asoundboard for the impact of the ideas of each respective discipline. We believe that goal was accomplished. but time will be a better judge. We have included the list of participants at the workshop. with most of these giving a presentation. Although the proceedings do not include all of the presentations. it is a good representative sampie. We wish to express our gratitude to NATO. and.to Dr. M. di Lullo of NATO. who unfortunately did not live to see the completion of this project.

Dynamics in Infinite Dimensions

Author : Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 51,7 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387228969

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Dynamics in Infinite Dimensions by Jack K. Hale,Luis T. Magalhaes,Waldyr Oliva Pdf

State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

Infinite Dimensional Dynamical Systems

Author : John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 54,9 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9781461445227

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Infinite Dimensional Dynamical Systems by John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi Pdf

​This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.​

Infinite-Dimensional Dynamical Systems in Mechanics and Physics

Author : Roger Temam
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 51,8 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461206453

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Infinite-Dimensional Dynamical Systems in Mechanics and Physics by Roger Temam Pdf

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.

Infinite-Dimensional Dynamical Systems

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 488 pages
File Size : 55,5 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521632048

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Infinite-Dimensional Dynamical Systems by James C. Robinson Pdf

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Optimal Control Theory for Infinite Dimensional Systems

Author : Xungjing Li,Jiongmin Yong
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242604

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Optimal Control Theory for Infinite Dimensional Systems by Xungjing Li,Jiongmin Yong Pdf

Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.

Infinite-Dimensional Dynamical Systems

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 8 pages
File Size : 48,6 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521632048

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Infinite-Dimensional Dynamical Systems by James C. Robinson Pdf

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Introduction to the Theory of Infinite-dimensional Dissipative Systems

Author : Igor' D. Čuešov,Igor Chueshov
Publisher : "Acta" publishers
Page : 421 pages
File Size : 41,6 Mb
Release : 2002
Category : Differentiable dynamical systems
ISBN : 9789667021641

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Introduction to the Theory of Infinite-dimensional Dissipative Systems by Igor' D. Čuešov,Igor Chueshov Pdf

Infinite-dimensional Dynamical Systems In Atmospheric And Oceanic Science

Author : Boling Guo,Daiwen Huang
Publisher : World Scientific
Page : 328 pages
File Size : 51,5 Mb
Release : 2014-04-17
Category : Mathematics
ISBN : 9789814590396

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Infinite-dimensional Dynamical Systems In Atmospheric And Oceanic Science by Boling Guo,Daiwen Huang Pdf

The book provides some recent works in the study of some infinite-dimensional dynamical systems in atmospheric and oceanic science. It devotes itself to considering some infinite-dimensional dynamical systems in atmospheric and oceanic science, especially in geophysical fluid dynamics. The subject on geophysical fluid dynamics mainly tends to focus on the dynamics of large-scale phenomena in the atmosphere and the oceans. One of the important contents in the dynamics is to study the infinite-dimensional dynamical systems of the atmospheric and oceanic dynamics. The results in the study of some partial differential equations of geophysical fluid dynamics and their corresponding infinite-dimensional dynamical systems are also given.

Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems

Author : Thomas Meurer,Knut Graichen,Ernst-Dieter Gilles
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 45,7 Mb
Release : 2005-09-19
Category : Technology & Engineering
ISBN : 3540279385

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Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems by Thomas Meurer,Knut Graichen,Ernst-Dieter Gilles Pdf

This volume presents a well balanced combination of state-of-the-art theoretical results in the field of nonlinear controller and observer design, combined with industrial applications stemming from mechatronics, electrical, (bio–) chemical engineering, and fluid dynamics. The unique combination of results of finite as well as infinite–dimensional systems makes this book a remarkable contribution addressing postgraduates, researchers, and engineers both at universities and in industry. The contributions to this book were presented at the Symposium on Nonlinear Control and Observer Design: From Theory to Applications (SYNCOD), held September 15–16, 2005, at the University of Stuttgart, Germany. The conference and this book are dedicated to the 65th birthday of Prof. Dr.–Ing. Dr.h.c. Michael Zeitz to honor his life – long research and contributions on the fields of nonlinear control and observer design.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics

Author : Roger Temam
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468403138

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Infinite-Dimensional Dynamical Systems in Mechanics and Physics by Roger Temam Pdf

This is the first attempt at a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics. Other areas of science and technology are included where appropriate. The relation between infinite and finite dimensional systems is presented from a synthetic viewpoint and equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau, damped wave and an introduction to inertial manifolds.

Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems

Author : Igor Chueshov,Björn Schmalfuß
Publisher : Springer
Page : 329 pages
File Size : 51,8 Mb
Release : 2021-07-30
Category : Mathematics
ISBN : 3030470938

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Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems by Igor Chueshov,Björn Schmalfuß Pdf

The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph presentation on both general and abstract models and covers several important classes of coupled nonlinear deterministic and stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts readily to advanced graduate coursework in dissipative dynamics, requires some background knowledge in evolutionary equations and introductory functional analysis as well as a basic understanding of PDEs and the theory of random processes. Suitable for researchers in synchronization theory, the book is also relevant to physicists and engineers interested in both the mathematical background and the methods for the asymptotic analysis of coupled infinite-dimensional dissipative systems that arise in continuum mechanics.

Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems

Author : Igor Chueshov,Björn Schmalfuß
Publisher : Springer Nature
Page : 346 pages
File Size : 48,7 Mb
Release : 2020-07-29
Category : Mathematics
ISBN : 9783030470913

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Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems by Igor Chueshov,Björn Schmalfuß Pdf

The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph presentation on both general and abstract models and covers several important classes of coupled nonlinear deterministic and stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts readily to advanced graduate coursework in dissipative dynamics, requires some background knowledge in evolutionary equations and introductory functional analysis as well as a basic understanding of PDEs and the theory of random processes. Suitable for researchers in synchronization theory, the book is also relevant to physicists and engineers interested in both the mathematical background and the methods for the asymptotic analysis of coupled infinite-dimensional dissipative systems that arise in continuum mechanics.

The Geometry of Infinite-Dimensional Groups

Author : Boris Khesin,Robert Wendt
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 40,9 Mb
Release : 2008-09-28
Category : Mathematics
ISBN : 9783540772637

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The Geometry of Infinite-Dimensional Groups by Boris Khesin,Robert Wendt Pdf

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.

Infinite Dimensional Optimization and Control Theory

Author : Hector O. Fattorini
Publisher : Cambridge University Press
Page : 828 pages
File Size : 47,8 Mb
Release : 1999-03-28
Category : Computers
ISBN : 0521451256

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Infinite Dimensional Optimization and Control Theory by Hector O. Fattorini Pdf

Treats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.