Lectures On Nonlinear Wave Equations
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Lectures On Non Linear Wave Equations
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Author : Christopher Donald Sogge
language : en
Publisher:
Release Date : 2008
Lectures On Non Linear 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 2008 with Mathematics categories.
Presents an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. This book examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced.
Lectures On Nonlinear Hyperbolic Differential Equations
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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-17
Lectures On Nonlinear Hyperbolic Differential Equations written by Lars Hörmander 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 1997-07-17 with Mathematics categories.
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.
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.
Nonlinear Wave Equations
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Author : Tatsien Li
language : en
Publisher: Springer
Release Date : 2017-11-23
Nonlinear Wave Equations written by Tatsien Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Mathematics categories.
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Nonlinear Wave Equations
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Author : Walter A. Strauss
language : en
Publisher: American Mathematical Soc.
Release Date : 1990-01-12
Nonlinear Wave Equations written by Walter A. Strauss 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 1990-01-12 with Mathematics categories.
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.
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.
Nonlinear Wave Equations
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Author : Yan Guo
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Nonlinear Wave Equations written by Yan Guo 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 2000 with Science categories.
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.
Nonlinear Evolution Equations Global Behavior Of Solutions
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Author : Alain Haraux
language : en
Publisher: Springer
Release Date : 2006-11-15
Nonlinear Evolution Equations Global Behavior Of Solutions written by Alain Haraux and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Nonlinear Wave Equations Formation Of Singularities
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Author : Fritz John
language : en
Publisher: American Mathematical Soc.
Release Date : 1990-07-01
Nonlinear Wave Equations Formation Of Singularities written by Fritz John 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 1990-07-01 with Mathematics categories.
This is the second volume in the University Lecture Series, designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher lectures presented by Fritz John in April 1989. The lectures deal with existence in the large of solutions of initial value problems for nonlinear hyperbolic partial differential equations. As is typical with nonlinear problems, there are many results and few general conclusions in this extensive subject, so the author restricts himself to a small portion of the field, in which it is possible to discern some general patterns. Presenting an exposition of recent research in this area, the author examines the way in which solutions can, even with small and very smooth initial data, ``blow up'' after a finite time. For various types of quasi-linear equations, this time depends strongly on the number of dimensions and the ``size'' of the data. Of particular interest is the formation of singularities for nonlinear wave equations in three space dimensions.
Lectures On Nonlinear Waves And Shocks
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Author : Cathleen S. Morawetz
language : en
Publisher:
Release Date : 1981
Lectures On Nonlinear Waves And Shocks written by Cathleen S. Morawetz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.