Nonlinear wave equations, formation of singularities
Author(s)
Bibliographic Information
Nonlinear wave equations, formation of singularities
(University lecture series, 2)
American Mathematical Society, c1990
Available at 67 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
At head of title: Pitcher lectures in the mathematical sciences, Lehigh University
"Revised notes of the Seventh Annual Pitcher lectures delivered at Lehigh University in April 1989"--Pref
Bibliography: p. 62-64
Description and Table of Contents
Description
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
Equations in one space variable Blow-up in higher dimensions Longtime existence for solutions of nonlinear wave equations with small initial data Appendix I. Uniqueness for nonlinear wave equations Appendix II. Klainerman's inequality.
by "Nielsen BookData"