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Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 41,9 Mb
Release : 1989
Category : Differentiable dynamical systems
ISBN : OCLC:636776945
Author : Basil Nicolaenko,Ciprian Foiaş
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 44,5 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821851050
The last few years have seen a number of major developments demonstrating that the long-term behavior of solutions of a very large class of partial differential equations possesses a striking resemblance to the behavior of solutions of finite dimensional dynamical systems, or ordinary differential equations. The first of these advances was the discovery that a dissipative PDE has a compact, global attractor with finite Hausdorff and fractal dimensions. More recently, it was shown that some of these PDEs possess a finite dimensional inertial manifold-that is, an invariant manifold containing the attractor and exponentially attractive trajectories. With the improved understanding of the exact connection between finite dimensional dynamical systems and various classes of dissipative PDEs, it is now realistic to hope that the wealth of studies of such topics as bifurcations of finite vector fields and ``strange'' fractal attractors can be brought to bear on various mathematical models, including continuum flows. Surprisingly, a number of distributed systems from continuum mechanics have been found to exhibit the same nontrivial dynamic behavior as observed in low-dimensional dynamical systems. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems. This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, 1987 at the University of Colorado at Boulder. Bringing together mathematicians and physicists, the conference provided a forum for presentations on the latest developments in the field and fostered lively interactions on open questions and future directions. With contributions from some of the top experts, these proceedings will provide readers with an overview of this vital area of research.
Author : James C. Robinson
Publisher : Cambridge University Press
Page : 488 pages
File Size : 44,8 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521632048
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.
Author : Basil Nicolaenko
Publisher : Unknown
Page : 0 pages
File Size : 43,5 Mb
Release : 1989
Category : Electronic
ISBN : 0821851055
Author : Roger Temam
Publisher : Springer Science & Business Media
Page : 670 pages
File Size : 44,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461206453
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.
Author : J.K. Hale,L.T. Magalhaes,W.M. Oliva
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 52,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475744934
Including: An Introduction to the Homotopy Theory in Noncompact Spaces
Author : Igor' D. Čuešov,Igor Chueshov
Publisher : "Acta" publishers
Page : 421 pages
File Size : 49,5 Mb
Release : 2002
Category : Differentiable dynamical systems
ISBN : 9789667021641
Author : Igor Chueshov,Björn Schmalfuß
Publisher : Springer Nature
Page : 346 pages
File Size : 52,7 Mb
Release : 2020-07-29
Category : Mathematics
ISBN : 9783030470913
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.
Author : James Robinson,Paul Glendinning
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 40,6 Mb
Release : 2001-05-31
Category : Mathematics
ISBN : 0792369750
This volume contains six papers originally presented at a NATO Advanced Study Institute held in Cambridge, U.K. in 1995 on the fundamental properties of partial differential equations and modeling processes involving spatial dynamics. The contributors, from academic institutions in Europe and the U.S., discuss such topics as lattice dynamical systems, low-dimensional models of turbulence, and nonlinear dynamics of extended systems. The volume is not indexed. c. Book News Inc.
Author : John Mallet-Paret,Jianhong Wu,Huaiping Zhu,Yingfie Yi
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 53,8 Mb
Release : 2012-10-11
Category : Mathematics
ISBN : 9781461445227
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.
Author : Wilfried Grecksch,Hannelore Lisei
Publisher : World Scientific
Page : 261 pages
File Size : 53,8 Mb
Release : 2020-04-22
Category : Science
ISBN : 9789811209802
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Author : Alain Bensoussan,Giuseppe Da Prato,Michel C. Delfour,Sanjoy K. Mitter
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 44,8 Mb
Release : 2007-04-05
Category : Technology & Engineering
ISBN : 9780817645816
This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Author : Michael I. Gil'
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461555759
The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Author : Alain Bensoussan,Giuseppe Da Prato,Michel C. Delfour,Sanjoy K. Mitter
Publisher : Birkhäuser
Page : 0 pages
File Size : 54,7 Mb
Release : 2008-11-01
Category : Technology & Engineering
ISBN : 0817671153
This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Author : Shui-Nee Chow,Jack K. Hale
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783642864582
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.