Advances in the theory of shock waves
Author(s)
Bibliographic Information
Advances in the theory of shock waves
(Progress in nonlinear differential equations and their applications / editor, Haim Brezis, 47)
Birkhäuser, c2001
Available at 26 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
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
LIU||11||2200021326234
Note
Includes bibliographical references
Description and Table of Contents
Description
In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.
Table of Contents
Preface * 'Well-Posedness Theory for a System of Hyperbolic Conservation Laws' / T.-P. LIU * 'Stability of Multidimensional Shocks' / G. METIVIER * 'Shock Wave Solutions of the Einstein Equations: A General Theory with Examples' / J. SMOLLER and B. TEMPLE * 'Basic Aspects of Hyperbolic Relaxation Systems' / W.-A. YONG * 'Multidimensional Stability of Planar Viscous Shock Waves' / K. ZUMBRUN
by "Nielsen BookData"