Lectures On The Energy Critical Nonlinear Wave Equation
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Lectures On The Energy Critical Nonlinear Wave Equation
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Author : Carlos E. Kenig
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-14
Lectures On The Energy Critical Nonlinear Wave Equation written by Carlos E. Kenig 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 2015-04-14 with Mathematics categories.
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.
Harmonic Analysis And Wave Equations
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Author : Jean-michel Coron
language : en
Publisher: World Scientific
Release Date : 2019-08-19
Harmonic Analysis And Wave Equations written by Jean-michel Coron and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-19 with Science categories.
This book is a collection of lecture notes for the LIASFMA School and Workshop on 'Harmonic Analysis and Wave Equations' which was held on May 8-18, 2017 at Fudan University, in Shanghai, China. The aim of the LIASFMA School and Workshop is to bring together Chinese and French experts to discuss and dissect recent progress in these related fields; and to disseminate state of art, new knowledge and new concepts, to graduate students and junior researchers.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in nonlinear wave-type equations. The readers will witness the major development with the introduction of modern harmonic analysis and related techniques.
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures
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Author : Rajendra Bhatia
language : en
Publisher: World Scientific
Release Date : 2011-06-06
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Rajendra Bhatia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Regularity And Scattering Of Dispersive Wave Equations
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Author : Changxing Miao
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-02-17
Regularity And Scattering Of Dispersive Wave Equations written by Changxing Miao 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 2025-02-17 with Mathematics categories.
The book places emphasis on both the mathematical significance and the strong physical background of wave equations. It presents the theory of wave equations in a unique way, different from the traditional descriptions provided by previous literature. The book is primarily focused on mathematical ideas and thoughts about wave equations. Starting from the modern theory of harmonic analysis, the book develops a few new tools in this field that are being used for better understanding the theory of mathematical physics underlying the well-posedness and scattering theory of wave and Klein-Gordon equations. Additionally, a significant part of this book discusses theories and methods, such as invariant and conservation laws, inward/outward energy methods, etc., that have never been covered by similar books in this field. Finally, the book briefly introduces recent developments in mathematical fields. It is specially designed for experts in mathematics and physics who deal with numerous applications of nonlinear waves in physics, engineering, biology, and other fields.
Dispersive Equations And Nonlinear Waves
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Author : Herbert Koch
language : en
Publisher: Springer
Release Date : 2014-07-14
Dispersive Equations And Nonlinear Waves written by Herbert Koch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.
Evolution Equations
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Author : David Ellwood
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-26
Evolution Equations written by David Ellwood 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 2013-06-26 with Mathematics categories.
This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Nonlinear Partial Differential Equations
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Author : Luis A. Caffarelli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-02
Nonlinear Partial Differential Equations written by Luis A. Caffarelli 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 2012-02-02 with Mathematics categories.
The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles.
Lectures On Nonlinear Wave Equations
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Author : Christopher Donald Sogge
language : en
Publisher:
Release Date : 1995
Lectures On Nonlinear Wave Equations written by Christopher Donald Sogge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This work presents three types of problems in the theory of nonlinear wave equations that have varying degrees of non-trivial overlap with harmonic analysis. The author discusses results including existence for certain quasilinear wave equations and for semilinear wave equations.
Harmonic Analysis Methods In Partial Differential Equations
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Author : Changxing Miao
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-06-02
Harmonic Analysis Methods In Partial Differential Equations written by Changxing Miao 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 2025-06-02 with Mathematics categories.
This volume applies theories of harmonic analysis to the study of nonlinear partial differential equations. It covers consolidation characterizations of differentiable function spaces, and the theory of three generations of C-Z singular integral operators, Fourier restriction estimation, Strichartz estimation, and Littlewood-Paley theory. It combines harmonic analysis methods with the study of partial differential equations.
Introduction To Nonlinear Dispersive Equations
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Author : Felipe Linares
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-21
Introduction To Nonlinear Dispersive Equations written by Felipe Linares 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 2009-02-21 with Mathematics categories.
The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schrodinger equation to describe properties enjoyed by general dispersive equations. This information is then used to treat local and global well-posedness for the semi-linear Schrodinger equations. The end of each chapter contains recent developments and open problems, as well as exercises.