The hyperbolic Cauchy problem

Author(s)

• 梶谷, 邦彦 カジタニ, クニヒコ
• 西谷, 達雄 ニシタニ, タツオ

Bibliographic Information

The hyperbolic Cauchy problem

Kunihiko Kajitani, Tatsuo Nishitani

（Lecture notes in mathematics, 1505 . Scuola normale superiore, Pisa）

Springer-Verlag, c1991

• : gw
• : us

Note

Bibliographical references: p. 166-167

Includes index

Description and Table of Contents

Description

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.

Table of Contents

Fourier integral operators with complex-valued phase function and the Cauchy problem for hyperbolic operators.- The effectively hyperbolic Cauchy problem.

by "Nielsen BookData"

Details

• NCID: BA13469158
• ISBN:
  • 3540550186
  • 0387550186
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: vi, 167 p.
• Size: 25 cm
• Classification:
  • NDC8 : 410.8
• Subject Headings:
  • LCSH : Cauchy problem
• Parent Bibliography ID:
  • BA00146586