Invariant Manifolds And Dispersive Hamiltonian Evolution Equations
DOWNLOAD
FREE 30 Days
Download Invariant Manifolds And Dispersive Hamiltonian Evolution Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Invariant Manifolds And Dispersive Hamiltonian Evolution Equations 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
Invariant Manifolds And Dispersive Hamiltonian Evolution Equations
DOWNLOAD
FREE 30 Days
Author : Kenji Nakanishi
language : en
Publisher: European Mathematical Society
Release Date : 2011
Invariant Manifolds And Dispersive Hamiltonian Evolution Equations written by Kenji Nakanishi and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Hamiltonian systems categories.
The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. The authors' entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors. The proofs rely on an interplay between the variational structure of the ground states and the nonlinear hyperbolic dynamics near these states. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.
Attractors Of Hamiltonian Nonlinear Partial Differential Equations
DOWNLOAD
FREE 30 Days
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.
This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.
Attractors Of Evolution Equations
DOWNLOAD
FREE 30 Days
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.
Systems Of Evolution Equations With Periodic And Quasiperiodic Coefficients
DOWNLOAD
FREE 30 Days
Author : I︠U︡riĭ Alekseevich Mitropolʹskiĭ
language : en
Publisher: Springer Science & Business Media
Release Date : 1993
Systems Of Evolution Equations With Periodic And Quasiperiodic Coefficients written by I︠U︡riĭ Alekseevich Mitropolʹskiĭ 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 1993 with Mathematics categories.
Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems.
Invariant Manifolds And Fibrations For Perturbed Nonlinear Schr Dinger Equations
DOWNLOAD
FREE 30 Days
Author : Charles Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Invariant Manifolds And Fibrations For Perturbed Nonlinear Schr Dinger Equations written by Charles Li 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 2012-12-06 with Mathematics categories.
In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds. Their techniques are based on an infinite dimensional generalisation of the graph transform and can be viewed as an infinite dimensional generalisation of Fenichels results. As such, they may be applied to a broad class of infinite dimensional dynamical systems.
Pde Dynamics
DOWNLOAD
FREE 30 Days
Author : Christian Kuehn
language : en
Publisher: SIAM
Release Date : 2019-04-10
Pde Dynamics written by Christian Kuehn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Geometric Numerical Integration And Schr Dinger Equations
DOWNLOAD
FREE 30 Days
Author : Erwan Faou
language : en
Publisher: European Mathematical Society
Release Date : 2012
Geometric Numerical Integration And Schr Dinger Equations written by Erwan Faou and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Numerical integration categories.
The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long periods of time. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long periods of time. In this setting, a natural question is how and to which extent the reproduction of such long-time qualitative behavior can be ensured by numerical schemes. Starting from numerical examples, these notes provide a detailed analysis of the Schrodinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations are provided for them. The book grew out of a graduate-level course and is of interest to researchers and students seeking an introduction to the subject matter.
Xviith International Congress On Mathematical Physics
DOWNLOAD
FREE 30 Days
Author : Arne Jensen
language : en
Publisher: World Scientific
Release Date : 2014
Xviith International Congress On Mathematical Physics written by Arne Jensen 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 with Science categories.
This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.
Topics In Occupation Times And Gaussian Free Fields
DOWNLOAD
FREE 30 Days
Author : Alain-Sol Sznitman
language : en
Publisher: European Mathematical Society
Release Date : 2012
Topics In Occupation Times And Gaussian Free Fields written by Alain-Sol Sznitman and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Gaussian processes categories.
This book grew out of a graduate course at ETH Zurich during the spring 2011 term. It explores various links between such notions as occupation times of Markov chains, Gaussian free fields, Poisson point processes of Markovian loops, and random interlacements, which have been the object of intensive research over the last few years. These notions are developed in the convenient setup of finite weighted graphs endowed with killing measures. This book first discusses elements of continuous-time Markov chains, Dirichlet forms, potential theory, together with some consequences for Gaussian free fields. Next, isomorphism theorems and generalized Ray-Knight theorems, which relate occupation times of Markov chains to Gaussian free fields, are presented. Markovian loops are constructed and some of their key properties derived. The field of occupation times of Poisson point processes of Markovian loops is investigated. Of special interest are its connection to the Gaussian free field, and a formula of Symanzik. Finally, links between random interlacements and Markovian loops are discussed, and some further connections with Gaussian free fields are mentioned.
Classical And Multilinear Harmonic Analysis
DOWNLOAD
FREE 30 Days
Author : Camil Muscalu
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
Classical And Multilinear Harmonic Analysis written by Camil Muscalu 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 2013-01-31 with Mathematics categories.
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.