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.
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.
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 488 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.
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:
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.
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:
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
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 496 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.
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:
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.
Download or read book Attractors for infinite dimensional non autonomous dynamical systems written by Alexandre Carvalho and published by Springer Science & Business Media. This book was released on 2012-09-25 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.
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
Download or read book From Finite to Infinite Dimensional Dynamical Systems written by James Robinson and published by Springer. This book was released on 2001-06-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures in this volume were given as part of a NATO Advanced Study Institute From finite to infinite dimensional dynamical systems held at the Isaac Newton Institute for Mathematical Sciences, Cambridge, U. K. , between 21 August and 1 September 1995. The NATO ASI brought together over sixty young scientists and mathematicians from all over the world to listen to expository talks from leading experts in the field, and also gave them the opportunity to present some of their own results as posters or as lectures. We hope that what they learned both formally and in informal conversations, and the friendships made during their stay in Cambridge, will remain important to them for many years to come. The NATO ASI formed part of a larger six month project at the New ton Institute on the same topic, and many of the participants were able to stay on in Cambridge to attend a Euro-Conference and both hear and contribute to the research in progress which was reported. We are grateful to all the bodies which helped fund these enterprises; principally, of course, NATO, but the European Union, CNRS (France) and the London Mathe matical Society all made contributions which allowed participants to stay on for the research conference and the Leverhume Trust funded the visits of participants from the former Soviet Union.
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.
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 1998-09-30 with total page 386 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.
Download or read book Linear Port Hamiltonian Systems on Infinite dimensional Spaces written by Birgit Jacob and published by Springer Science & Business Media. This book was released on 2012-06-13 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.
Download or read book Representation and Control of Infinite Dimensional Systems written by Alain Bensoussan and published by Birkhäuser. This book was released on 2008-11-01 with total page 0 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.
