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Invariant Wave Equations
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Book Synopsis Nonlinear Wave Equations by : Walter A. Strauss
Download or read book Nonlinear Wave Equations written by Walter A. Strauss and published by American Mathematical Soc.. This book was released on 1990-01-12 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
Book Synopsis Blowup for Nonlinear Hyperbolic Equations by : Serge Alinhac
Download or read book Blowup for Nonlinear Hyperbolic Equations written by Serge Alinhac and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solutions to partial differential equations or systems often, over specific time periods, exhibit smooth behaviour. Given sufficient time, however, they almost invariably undergo a brutal change in behaviour, and this phenomenon has become known as blowup. In this book, the author provides an overview of what is known about this situation and discusses many of the open problems concerning it.
Book Synopsis Invariant Manifolds and Dispersive Hamiltonian Evolution Equations by : Kenji Nakanishi
Download or read book Invariant Manifolds and Dispersive Hamiltonian Evolution Equations written by Kenji Nakanishi and published by European Mathematical Society. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Wave Equations by : Jalal M. Ihsan Shatah
Download or read book Geometric Wave Equations written by Jalal M. Ihsan Shatah and published by American Mathematical Soc.. This book was released on 2000 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the recent work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Book Synopsis New Tools for Nonlinear PDEs and Application by : Marcello D'Abbicco
Download or read book New Tools for Nonlinear PDEs and Application written by Marcello D'Abbicco and published by Springer. This book was released on 2019-05-07 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.
Book Synopsis Nonlinear Wave Equations by : Yan Guo
Download or read book Nonlinear Wave Equations written by Yan Guo and published by American Mathematical Soc.. This book was released on 2000 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents original research papers and expository articles from the conference in honour of Walter A. Strauss's 60th birthday, held at Brown University in Providence, Rhode Island. The book offers a collection of original papers and expository articles mainly devoted to the study of nonlinear wave equations. The articles cover a wide range of topics, including scattering theory, dispersive waves, classical field theory, mathematical fluid dynamics, kinetic theory, stability theory, and variational methods. The book offers a cross-section of current trends and research directions in the study of nonlinear wave equations and related topics.
Book Synopsis Lectures on the Energy Critical Nonlinear Wave Equation by : Carlos E. Kenig
Download or read book Lectures on the Energy Critical Nonlinear Wave Equation written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2015-04-14 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the "concentration-compactness/rigidity theorem method" introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the "global regularity and well-posedness" conjecture (defocusing case) and the "ground-state" conjecture (focusing case) in critical dispersive problems. The second part of the monograph describes the "channel of energy" method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the three-dimensional radial focusing energy critical wave equation. It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations. A co-publication of the AMS and CBMS.
Book Synopsis The Theory of Symmetry Actions in Quantum Mechanics by : Gianni Cassinelli
Download or read book The Theory of Symmetry Actions in Quantum Mechanics written by Gianni Cassinelli and published by Springer Science & Business Media. This book was released on 2004-10-27 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given.
Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos
Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Gulf Professional Publishing. This book was released on 2005-11-30 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous, and in depth surveys on the most important aspects of the present theory.
Book Synopsis Library of Congress Subject Headings by : Library of Congress
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2013 with total page 1480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Nonlinear Hyperbolic Differential Equations by : Lars Hörmander
Download or read book Lectures on Nonlinear Hyperbolic Differential Equations written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 1997-07-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.
Book Synopsis Problems in Quantum Mechanics and Field Theory with Mathematical Modelling by : Aleksander V. Chichurin
Download or read book Problems in Quantum Mechanics and Field Theory with Mathematical Modelling written by Aleksander V. Chichurin and published by CRC Press. This book was released on 2024-10-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Problems in Quantum Mechanics and Field Theory with Mathematical Modelling, a number of exactly solvable problems in electrodynamics and in quantum-mechanics of particles with different spins are presented. The main topics covered include: the Cox scalar particle with intrinsic structure in presence of the magnetic field in the spaces of constant curvature, Euclid, Riemann, and Lobachevsky; Cox particle in the Coulomb field; tunneling effect through Schwarzschild barrier for a spin 1/2 particle; electromagnetic field in Schwarzschild space-time, the Majorana - Oppenheimer approach in electrodynamics; scalar particle with polarizability in the Coulomb field; Dirac particle in the Coulomb field on the background of hyperbolic Lobachevsky and spherical Riemann models; particle with spin 1 in the Coulomb field; geometrical modeling of the media in Maxwell electrodynamics; P-asymmetric equation for a spin 1/2 particle; fermion with two mass parameters in the Coulomb field; helicity operator for a spin 2 particle in presence of the magnetic field. The book will be of interest to researchers, and is accessible enough to serve as a self-study resources for courses at undergraduate and graduate levels.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1975-02 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Partial Differential Equations and Related Fields by : Andreas Eberle
Download or read book Stochastic Partial Differential Equations and Related Fields written by Andreas Eberle and published by Springer. This book was released on 2018-07-03 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
Book Synopsis III: Scattering Theory by : Michael Reed
Download or read book III: Scattering Theory written by Michael Reed and published by Elsevier. This book was released on 1979-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.
Book Synopsis Advances in Imaging and Electron Physics by :
Download or read book Advances in Imaging and Electron Physics written by and published by Academic Press. This book was released on 2012-12-02 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Imaging and Electron Physics features cutting-edge articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. - Contributions from leading authorities - Informs and updates on all the latest developments in the field
Book Synopsis Library of Congress Subject Headings by : Library of Congress. Cataloging Policy and Support Office
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2009 with total page 1924 pages. Available in PDF, EPUB and Kindle. Book excerpt:
