The hyperbolic Cauchy problem. Lecture notes in mathematics ; 1505 : Subseries: Scuola Normale Superiore, Pisa

Kajitani, Kunihiko und Tatsuo Nishitani,

ISBN 10: 3540550186 / ISBN 13: 9783540550181

Published by Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer, 1991

About this Item

VI, 167 pages Ex-Library book in good condition. 9783540550181 Sprache: Englisch Gewicht in Gramm: 330.

Seller Inventory # 1162207

Bibliographic Details

• Title: The hyperbolic Cauchy problem. Lecture notes in mathematics ; 1505 : Subseries: Scuola Normale Superiore, Pisa
• Publisher: Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest : Springer
• Publication Date: 1991
• Language: English
• ISBN 10: 3540550186
• ISBN 13: 9783540550181
• Binding: Soft cover
• Seller catalogs:
  • AA Varia

About this title

Synopsis

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.