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Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (636 download)
Download or read book The Connection Between Infinite Dimensional and Finite Dimensional Dynamical Systems written by and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Basil Nicolaenko
Publisher : American Mathematical Soc.
ISBN 13 : 0821851055
Total Pages : 380 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1989 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Basil Nicolaenko
Publisher :
ISBN 13 : 9780821851050
Total Pages : 0 pages
Book Rating : 4.8/5 (51 download)
Download or read book The Connection Between Infinite Dimensional and Finite Dimensional Dynamical Systems written by Basil Nicolaenko and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Robinson
Publisher : Springer Science & Business Media
ISBN 13 : 9780792369752
Total Pages : 240 pages
Book Rating : 4.3/5 (697 download)
Download or read book From Finite to Infinite Dimensional Dynamical Systems written by James Robinson and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : James C. Robinson
Publisher : Cambridge University Press
ISBN 13 : 9780521632041
Total Pages : 8 pages
Book Rating : 4.6/5 (32 download)
Download or read book Infinite-Dimensional Dynamical Systems written by James C. Robinson and published by Cambridge University Press. This book was released on 2001-04-23 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Roger Temam
Publisher : Springer Science & Business Media
ISBN 13 : 1461206456
Total Pages : 670 pages
Book Rating : 4.4/5 (612 download)
Download or read book Infinite-Dimensional Dynamical Systems in Mechanics and Physics written by Roger Temam and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 1475744935
Total Pages : 203 pages
Book Rating : 4.4/5 (757 download)
Download or read book An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory written by J.K. Hale and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including: An Introduction to the Homotopy Theory in Noncompact Spaces
Author : Igor' D. Čuešov
Publisher : "Acta" publishers
ISBN 13 : 9667021645
Total Pages : 421 pages
Book Rating : 4.6/5 (67 download)
Download or read book Introduction to the Theory of Infinite-dimensional Dissipative Systems written by Igor' D. Čuešov and published by "Acta" publishers. This book was released on 2002 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alain Bensoussan
Publisher : Springer Science & Business Media
ISBN 13 : 0817645810
Total Pages : 589 pages
Book Rating : 4.8/5 (176 download)
Download or read book Representation and Control of Infinite Dimensional Systems written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Igor Chueshov
Publisher : Springer Nature
ISBN 13 : 3030470911
Total Pages : 346 pages
Book Rating : 4.0/5 (34 download)
Download or read book Synchronization in Infinite-Dimensional Deterministic and Stochastic Systems written by Igor Chueshov and published by Springer Nature. This book was released on 2020-07-29 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Maxwell
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (227 download)
Download or read book Infinite Dimensional Dynamical Systems and Their Finite Dimensional Analogues written by Maxwell and published by . This book was released on 1987 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The speakers gave reports on their research to-date concerning nonlinear Partial Differential Equations and possible systems of Ordinary Differential Equations which faithfully capture their essential behavior, particularly in terms of chaotic behavior.
Author : John Mallet-Paret
Publisher : Springer Science & Business Media
ISBN 13 : 146144523X
Total Pages : 495 pages
Book Rating : 4.4/5 (614 download)
Download or read book Infinite Dimensional Dynamical Systems written by John Mallet-Paret and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 0387954635
Total Pages : 287 pages
Book Rating : 4.3/5 (879 download)
Download or read book Dynamics in Infinite Dimensions written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2002-07-12 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Wilfried Grecksch
Publisher : World Scientific
ISBN 13 : 9811209804
Total Pages : 261 pages
Book Rating : 4.8/5 (112 download)
Download or read book Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and published by World Scientific. This book was released on 2020-04-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Adrian Ziessler
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)
Download or read book Analysis of Infinite Dimensional Dynamical Systems by Set-oriented Numerics written by Adrian Ziessler and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: One central goal in the analysis of dynamical systems is the characterization of long term behavior of the system state. To this end, the so-called global attractor is of interest, that is, an invariant set that attracts all the trajectories of the underlying dynamical system. Over the last 20 years so-called set-oriented numerical methods have been developed that allow to compute approximations of invariant sets. The basic idea is to cover the objects of interest, for instance attractors or unstable manifolds, by outer approximations which are created via subdivision techniques. However, the applicability of those techniques is restricted to finite dimensional dynamical systems, i.e., ordinary differential equations or discrete dynamical systems. In this thesis, we extend the set-oriented numerical methods to the infinite dimensional context. With those extensions we will be able to compute finite dimensional invariant sets for infinite dimensional dynamical systems, e.g., for delay and partial differential equations. The idea is to utilize infinite dimensional embedding techniques in our numerical treatment. This will allow us to construct a finite dimensional dynamical system, the core dynamical system (CDS), on an appropriately chosen observation space. Using the CDS, we then can approximate finite dimensional embedded attractors or embedded unstable manifolds. Furthermore, we will be able to compute approximations of the embedded invariant measure in the observation space which gives a statistical description of the dynamical behavior of the infinite dimensional dynamical system. We present numerical realizations of the CDS for delay and partial differential equations and illustrate the efficiency of our approach in several examples. Furthermore, we present modifications for the set-oriented subdivision and continuation method. ... ; eng
Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 0387228969
Total Pages : 286 pages
Book Rating : 4.3/5 (872 download)
Download or read book Dynamics in Infinite Dimensions written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Michael I. Gil'
Publisher : Springer Science & Business Media
ISBN 13 : 1461555752
Total Pages : 363 pages
Book Rating : 4.4/5 (615 download)
Download or read book Stability of Finite and Infinite Dimensional Systems written by Michael I. Gil' and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
