SoftcoverISBN:  9780821841433 
Product Code:  CBMS/106 
List Price:  $57.00 
Individual Price:  $45.60 
eBookISBN:  9781470424664 
Product Code:  CBMS/106.E 
List Price:  $57.00 
Individual Price:  $45.60 
SoftcoverISBN:  9780821841433 
eBookISBN:  9781470424664 
Product Code:  CBMS/106.B 
List Price:  $114.00$85.50 
Softcover ISBN:  9780821841433 
Product Code:  CBMS/106 
List Price:  $57.00 
Individual Price:  $45.60 
eBook ISBN:  9781470424664 
Product Code:  CBMS/106.E 
List Price:  $57.00 
Individual Price:  $45.60 
Softcover ISBN:  9780821841433 
eBookISBN:  9781470424664 
Product Code:  CBMS/106.B 
List Price:  $114.00$85.50 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 106; 2006; 373 ppMSC: Primary 35;
Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations.
Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the realworld intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.
As the subject is vast, the book does not attempt to give a comprehensive survey of the field, but instead concentrates on a representative sample of results for a selected set of equations, ranging from the fundamental local and global existence theorems to very recent results, particularly focusing on the recent progress in understanding the evolution of energycritical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE.ReadershipGraduate students and research mathematicians interested in nonlinear partial differential equations.

Table of Contents

Chapters

Chapter 1. Ordinary differential equations

Chapter 2. Constant coefficient linear dispersive equations

Chapter 3. Semilinear dispersive equations

Chapter 4. The Korteweg de Vries equation

Chapter 5. Energycritical semilinear dispersive equations

Chapter 6. Wave maps

Appendix A. Tools from harmonic analysis

Appendix B. Construction of ground states


Additional Material

Reviews

Tao certainly succeeds in writing a vivid and instructional text on nonlinear dispersive partial differential equations. It touches on topics of recent research interest and is a valuable source both for the beginning graduate student and, to some extent, for the advanced researcher.
Mathematical Reviews 
The work is well suited for a graduate level course on nonlinear PDE, and it is to be thoroughly recommended.
Alan Jeffrey for Zentralblatt MATH


RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations.
Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the realworld intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.
As the subject is vast, the book does not attempt to give a comprehensive survey of the field, but instead concentrates on a representative sample of results for a selected set of equations, ranging from the fundamental local and global existence theorems to very recent results, particularly focusing on the recent progress in understanding the evolution of energycritical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE.
Graduate students and research mathematicians interested in nonlinear partial differential equations.

Chapters

Chapter 1. Ordinary differential equations

Chapter 2. Constant coefficient linear dispersive equations

Chapter 3. Semilinear dispersive equations

Chapter 4. The Korteweg de Vries equation

Chapter 5. Energycritical semilinear dispersive equations

Chapter 6. Wave maps

Appendix A. Tools from harmonic analysis

Appendix B. Construction of ground states

Tao certainly succeeds in writing a vivid and instructional text on nonlinear dispersive partial differential equations. It touches on topics of recent research interest and is a valuable source both for the beginning graduate student and, to some extent, for the advanced researcher.
Mathematical Reviews 
The work is well suited for a graduate level course on nonlinear PDE, and it is to be thoroughly recommended.
Alan Jeffrey for Zentralblatt MATH