Attractors And Inertial Manifolds
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Attractors and Inertial Manifolds
Author | : Boling Guo,Liming Ling,Yansheng Ma,Hui Yang |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 438 |
Release | : 2018-07-09 |
Genre | : Mathematics |
ISBN | : 9783110549652 |
Download Attractors and Inertial Manifolds Book in PDF, Epub and Kindle
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
Attractors and Inertial Manifolds
Author | : Boling Guo,Liming Ling,Yansheng Ma,Hui Yang |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 438 |
Release | : 2018-07-09 |
Genre | : Mathematics |
ISBN | : 9783110549423 |
Download Attractors and Inertial Manifolds Book in PDF, Epub and Kindle
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
Attractors and Methods
Author | : Boling Guo,Liming Ling,Yansheng Ma,Hui Yang |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 413 |
Release | : 2018-07-09 |
Genre | : Mathematics |
ISBN | : 9783110587265 |
Download Attractors and Methods Book in PDF, Epub and Kindle
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves
Infinite dimensional Dynamical Systems
Author | : Boling Guo,Liming Ling,Yansheng Ma,Hui Yang |
Publsiher | : de Gruyter |
Total Pages | : 0 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 3110549255 |
Download Infinite dimensional Dynamical Systems Book in PDF, Epub and Kindle
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
Author | : P. Constantin,C. Foias,B. Nicolaenko,R. Temam |
Publsiher | : Springer Science & Business Media |
Total Pages | : 133 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461235064 |
Download Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations Book in PDF, Epub and Kindle
This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.
Attractors and Methods
Author | : Boling Guo,Liming Ling,Yansheng Ma,Hui Yang |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 577 |
Release | : 2018-07-09 |
Genre | : Mathematics |
ISBN | : 9783110587081 |
Download Attractors and Methods Book in PDF, Epub and Kindle
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves
Mathematics of Climate Modeling
Author | : Valentin P. Dymnikov,Aleksander N. Filatov |
Publsiher | : Springer Science & Business Media |
Total Pages | : 275 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461241485 |
Download Mathematics of Climate Modeling Book in PDF, Epub and Kindle
The present monograph is dedicated to a new branch of the theory of climate, which is titled by the authors, "Mathematical Theory of Climate. " The foundation of this branch is the investigation of climate models by the methods of the qUalitative theory of differential equa tions. In the Russian edition the book was named "Fundamentals of the Mathematical Theory of Climate. " Respecting the recommenda tions of Wayne Yuhasz (we are truly grateful to him for this advice), we named the English edition of the book "Mathematics of Climate Modelling. " This title appears to be more appropriate, since the con structive results of the theory are at present preliminary and have not been fully tested with experiments in climate modelling. This branch of science is yet developing and its practical results will be obtained only in the near future. Nevertheless, we want to keep the terminology which we have used in the introduction to the Russian edition of the book, since the authors hope that this term will be accepted by the scientific community for identification of a given branch of climate theory. On preparing the English edition, new ideas were established con necting some significant new research results obtained by the author. We are deeply grateful to G. Marchuk for continual encourage ment of this scientific enterprise and fruitful discussions, to our young colleagues A. Gorelov, E. Kazantsev, A. Gritsun, and A.
Infinite Dimensional Dynamical Systems in Mechanics and Physics
Author | : Roger Temam |
Publsiher | : Springer Science & Business Media |
Total Pages | : 670 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 9781461206453 |
Download Infinite Dimensional Dynamical Systems in Mechanics and Physics Book in PDF, Epub and Kindle
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.