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Nonlinear Wave Equations, Formation of Singularities
 
Fritz John New York University-Courant Institute of Mathematical Sciences, New York, NY
Nonlinear Wave Equations, Formation of Singularities
Softcover ISBN:  978-0-8218-7001-3
Product Code:  ULECT/2
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
eBook ISBN:  978-1-4704-2155-7
Product Code:  ULECT/2.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-0-8218-7001-3
eBook: ISBN:  978-1-4704-2155-7
Product Code:  ULECT/2.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $107.20 $81.20
Nonlinear Wave Equations, Formation of Singularities
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Nonlinear Wave Equations, Formation of Singularities
Fritz John New York University-Courant Institute of Mathematical Sciences, New York, NY
Softcover ISBN:  978-0-8218-7001-3
Product Code:  ULECT/2
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
eBook ISBN:  978-1-4704-2155-7
Product Code:  ULECT/2.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-0-8218-7001-3
eBook ISBN:  978-1-4704-2155-7
Product Code:  ULECT/2.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $107.20 $81.20
  • Book Details
     
     
    University Lecture Series
    Volume: 21990; 64 pp
    MSC: Primary 35

    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.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter 1. Equations in one space variable
    • Chapter 2. Blow-up in higher dimensions
    • Chapter 3. Longtime existence for solutions of nonlinear wave equations with small initial data
    • Appendix 1. Uniqueness for nonlinear wave equations
    • Appendix 2. Klainerman’s inequality
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 21990; 64 pp
MSC: Primary 35

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.

  • Chapters
  • Introduction
  • Chapter 1. Equations in one space variable
  • Chapter 2. Blow-up in higher dimensions
  • Chapter 3. Longtime existence for solutions of nonlinear wave equations with small initial data
  • Appendix 1. Uniqueness for nonlinear wave equations
  • Appendix 2. Klainerman’s inequality
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.