Attractors For Equations Of Mathematical Physics
DOWNLOAD
Download Attractors For Equations Of Mathematical Physics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Attractors For Equations Of Mathematical Physics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Attractors For Equations Of Mathematical Physics
DOWNLOAD
Author : Vladimir V. Chepyzhov
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Attractors For Equations Of Mathematical Physics written by Vladimir V. Chepyzhov 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 2002 with Mathematics categories.
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For anumber of basic evolution equations of mathematical physics, it was shown that the long time behavior of their solutions can be characterized by a very important notion of a global attractor of the equation. In this book, the authors study new problems related to the theory of infinite-dimensionaldynamical systems that were intensively developed during the last 20 years. They construct the attractors and study their properties for various non-autonomous equations of mathematical physics: the 2D and 3D Navier-Stokes systems, reaction-diffusion systems, dissipative wave equations, the complex Ginzburg-Landau equation, and others. Since, as it is shown, the attractors usually have infinite dimension, the research is focused on the Kolmogorov $\varepsilon$-entropy of attractors. Upperestimates for the $\varepsilon$-entropy of uniform attractors of non-autonomous equations in terms of $\varepsilon$-entropy of time-dependent coefficients are proved. Also, the authors construct attractors for those equations of mathematical physics for which the solution of the corresponding Cauchyproblem is not unique or the uniqueness is not proved. The theory of the trajectory attractors for these equations is developed, which is later used to construct global attractors for equations without uniqueness. The method of trajectory attractors is applied to the study of finite-dimensional approximations of attractors. The perturbation theory for trajectory and global attractors is developed and used in the study of the attractors of equations with terms rapidly oscillating with respect tospatial and time variables. It is shown that the attractors of these equations are contained in a thin neighborhood of the attractor of the averaged equation. The book gives systematic treatment to the theory of attractors of autonomous and non-autonomous evolution equations of mathematical physics.It can be used both by specialists and by those who want to get acquainted with this rapidly growing and important area of mathematics.
Attractors Of Evolution Equations
DOWNLOAD
Author : A.V. Babin
language : en
Publisher: Elsevier
Release Date : 1992-03-09
Attractors Of Evolution Equations written by A.V. Babin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-09 with Mathematics categories.
Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes system, which attracts (in an appropriate functional space) as t - ∞ all trajectories of this system, is a compact finite-dimensional (in the sense of Hausdorff) set. Upper and lower bounds (in terms of the Reynolds number) for the dimension of the attractor were found. These results for the Navier-Stokes system have stimulated investigations of attractors of other equations of mathematical physics. For certain problems, in particular for reaction-diffusion systems and nonlinear damped wave equations, mathematicians have established the existence of the attractors and their basic properties; furthermore, they proved that, as t - +∞, an infinite-dimensional dynamics described by these equations and systems uniformly approaches a finite-dimensional dynamics on the attractor U, which, in the case being considered, is the union of smooth manifolds. This book is devoted to these and several other topics related to the behaviour as t - ∞ of solutions for evolutionary equations.
Attractors For Degenerate Parabolic Type Equations
DOWNLOAD
Author : Messoud Efendiev
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-09-26
Attractors For Degenerate Parabolic Type Equations written by Messoud Efendiev 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 2013-09-26 with Mathematics categories.
This book deals with the long-time behavior of solutions of degenerate parabolic dissipative equations arising in the study of biological, ecological, and physical problems. Examples include porous media equations, -Laplacian and doubly nonlinear equations, as well as degenerate diffusion equations with chemotaxis and ODE-PDE coupling systems. For the first time, the long-time dynamics of various classes of degenerate parabolic equations, both semilinear and quasilinear, are systematically studied in terms of their global and exponential attractors. The long-time behavior of many dissipative systems generated by evolution equations of mathematical physics can be described in terms of global attractors. In the case of dissipative PDEs in bounded domains, this attractor usually has finite Hausdorff and fractal dimension. Hence, if the global attractor exists, its defining property guarantees that the dynamical system reduced to the attractor contains all of the nontrivial dynamics of the original system. Moreover, the reduced phase space is really "thinner" than the initial phase space. However, in contrast to nondegenerate parabolic type equations, for a quite large class of degenerate parabolic type equations, their global attractors can have infinite fractal dimension. The main goal of the present book is to give a detailed and systematic study of the well-posedness and the dynamics of the semigroup associated to important degenerate parabolic equations in terms of their global and exponential attractors. Fundamental topics include existence of attractors, convergence of the dynamics and the rate of convergence, as well as the determination of the fractal dimension and the Kolmogorov entropy of corresponding attractors. The analysis and results in this book show that there are new effects related to the attractor of such degenerate equations that cannot be observed in the case of nondegenerate equations in bounded domains. This book is published in cooperation with Real Sociedad Matemática Española (RSME).
Attractors And Inertial Manifolds
DOWNLOAD
Author : Boling Guo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-07-09
Attractors And Inertial Manifolds written by Boling Guo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Mathematics categories.
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 Of Hamiltonian Nonlinear Partial Differential Equations
DOWNLOAD
Author : Alexander Komech
language : en
Publisher: Cambridge University Press
Release Date : 2021-09-30
Attractors Of Hamiltonian Nonlinear Partial Differential Equations written by Alexander Komech 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 2021-09-30 with Mathematics categories.
The first monograph on the theory of global attractors of Hamiltonian partial differential equations.
Attractors And Methods
DOWNLOAD
Author : Boling Guo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-07-09
Attractors And Methods written by Boling Guo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Mathematics categories.
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
Finite And Infinite Dimensional Attractors For Evolution Equations Of Mathematical Physics
DOWNLOAD
Author : Messoud Efendiev
language : ja
Publisher:
Release Date : 2010-11
Finite And Infinite Dimensional Attractors For Evolution Equations Of Mathematical Physics written by Messoud Efendiev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11 with categories.
Attractors For Semigroups And Evolution Equations
DOWNLOAD
Author : Olga A. Ladyzhenskaya
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Attractors For Semigroups And Evolution Equations written by Olga A. Ladyzhenskaya 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 2022-06-09 with Mathematics categories.
First published 1992; Re-issued 2008; Reprinted with Introduction 2022.
Lectures On Quantum Mechanics And Attractors
DOWNLOAD
Author : Alexander Komech
language : en
Publisher: World Scientific
Release Date : 2022-02-18
Lectures On Quantum Mechanics And Attractors written by Alexander Komech and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-18 with Science categories.
This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.
Properties Of Global Attractors Of Partial Differential Equations
DOWNLOAD
Author : Anatoliĭ Vladimirovich Babin
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Properties Of Global Attractors Of Partial Differential Equations written by Anatoliĭ Vladimirovich Babin 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 1992 with Attractors (Mathematics) categories.