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© 1993

Partial Differential Equations IV

Microlocal Analysis and Hyperbolic Equations

  • Yu. V. Egorov
  • M. A. Shubin
Book

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 33)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Yu. V. Egorov
    Pages 1-147
  3. V. Ya. Ivrii
    Pages 149-235
  4. Back Matter
    Pages 237-244

About this book

Introduction

In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics.

Keywords

Ausbreitung von Singularitäten C and L2 well posedness of the Cauchy problem Fourier integral operators Fourier-Integraloperatoren Gevrey classes Gevreysche Klassen Hamiltonian systems Hamiltonsche Systeme Hyperbolische Operatoren Hypoelliptizitä Microlocal analysis Theoretical physics calculus hyperbolic equation partial differential equation

Editors and affiliations

  • Yu. V. Egorov
    • 1
  • M. A. Shubin
    • 1
  1. 1.Department of MathematicsMoscow State University, Leninskie GoryMoscowRussia

Bibliographic information

  • Book Title Partial Differential Equations IV
  • Book Subtitle Microlocal Analysis and Hyperbolic Equations
  • Editors Yu.V. Egorov
    M.A. Shubin
  • Series Title Encyclopaedia of Mathematical Sciences
  • DOI https://doi.org/10.1007/978-3-662-09207-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-53363-4
  • Softcover ISBN 978-3-642-08099-9
  • eBook ISBN 978-3-662-09207-1
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages VIII, 244
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original Russian edition published by VINITI, Moscow, 1988
  • Topics Analysis
    Theoretical, Mathematical and Computational Physics
  • Buy this book on publisher's site