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Nonlinear Dispersive Equations: Local and Global Analysis
 
Terence Tao University of California, Los Angeles, Los Angeles, CA
A co-publication of the AMS and CBMS
Nonlinear Dispersive Equations
Softcover ISBN:  978-0-8218-4143-3
Product Code:  CBMS/106
List Price: $60.00
Individual Price: $48.00
eBook ISBN:  978-1-4704-2466-4
Product Code:  CBMS/106.E
List Price: $60.00
Individual Price: $48.00
Softcover ISBN:  978-0-8218-4143-3
eBook: ISBN:  978-1-4704-2466-4
Product Code:  CBMS/106.B
List Price: $120.00 $90.00
Nonlinear Dispersive Equations
Click above image for expanded view
Nonlinear Dispersive Equations: Local and Global Analysis
Terence Tao University of California, Los Angeles, Los Angeles, CA
A co-publication of the AMS and CBMS
Softcover ISBN:  978-0-8218-4143-3
Product Code:  CBMS/106
List Price: $60.00
Individual Price: $48.00
eBook ISBN:  978-1-4704-2466-4
Product Code:  CBMS/106.E
List Price: $60.00
Individual Price: $48.00
Softcover ISBN:  978-0-8218-4143-3
eBook ISBN:  978-1-4704-2466-4
Product Code:  CBMS/106.B
List Price: $120.00 $90.00
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 1062006; 373 pp
    MSC: 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 real-world 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 energy-critical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE.

    Readership

    Graduate 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. Energy-critical semilinear dispersive equations
    • Chapter 6. Wave maps
    • Appendix A. Tools from harmonic analysis
    • Appendix B. Construction of ground states
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1062006; 373 pp
MSC: 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 real-world 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 energy-critical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE.

Readership

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. Energy-critical 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.