Infinite Dimensional Dynamical Systems
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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 : 2013-12-11
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 2013-12-11 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.
Infinite Dimensional Dynamical Systems
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Author : John Mallet-Paret
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-11
Infinite Dimensional Dynamical Systems written by John Mallet-Paret 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 2012-10-11 with Mathematics categories.
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.
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems
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Author : Basil Nicolaenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems written by Basil Nicolaenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
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.
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 which 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 systems 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.
Infinite Dimensional Dynamical Systems
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Author : Boling Guo
language : en
Publisher:
Release Date : 2018
Infinite Dimensional Dynamical Systems written by Boling Guo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Infinite Dimensional Dynamical Systems In Atmospheric And Oceanic Science
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Author : Boling Guo
language : en
Publisher: World Scientific
Release Date : 2014-04-17
Infinite Dimensional Dynamical Systems In Atmospheric And Oceanic Science written by Boling Guo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-17 with Mathematics categories.
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.
From Finite To Infinite Dimensional Dynamical Systems
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Author : James Robinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-31
From Finite To Infinite Dimensional Dynamical Systems written by James Robinson 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 2001-05-31 with Mathematics categories.
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.
An Introduction To Infinite Dimensional Dynamical Systems Geometric Theory
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Author : J.K. Hale
language : en
Publisher: Springer
Release Date : 2013-02-14
An Introduction To Infinite Dimensional Dynamical Systems Geometric Theory written by J.K. Hale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-14 with Mathematics categories.
Including: An Introduction to the Homotopy Theory in Noncompact Spaces
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems
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Author :
language : en
Publisher:
Release Date : 1989
The Connection Between Infinite Dimensional And Finite Dimensional Dynamical Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Differentiable dynamical systems categories.
An Introduction To Infinite Dimensional Dynamical Systems Geometric Theory
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Author : Jack K. Hale
language : en
Publisher:
Release Date : 1984
An Introduction To Infinite Dimensional Dynamical Systems Geometric Theory written by Jack K. Hale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Differentiable dynamical systems categories.