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The Hyperbolic Cauchy Problem

  • Authors
  • Kunihiko¬†Kajitani
  • Tatsuo¬†Nishitani

Part of the Lecture Notes in Mathematics book series (LNM, volume 1505)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Tatsuo Nishitani
    Pages 71-167
  3. Back Matter
    Pages 168-168

About this book

Introduction

The approach to the Cauchy problem taken here by the authors is based on theuse of Fourier integral operators with a complex-valued phase function, which is a time function chosen suitably according to the geometry of the multiple characteristics. The correctness of the Cauchy problem in the Gevrey classes for operators with hyperbolic principal part is shown in the first part. In the second part, the correctness of the Cauchy problem for effectively hyperbolic operators is proved with a precise estimate of the loss of derivatives. This method can be applied to other (non) hyperbolic problems. The text is based on a course of lectures given for graduate students but will be of interest to researchers interested in hyperbolic partial differential equations. In the latter part the reader is expected to be familiar with some theory of pseudo-differential operators.

Keywords

Cauchy problem Derivative Hyperbolic operators differential equation hyperbolic partial differential equation partial differential equation partial differential equations phase function pseudo-differential operators

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0090882
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55018-1
  • Online ISBN 978-3-540-46655-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site