The Hyperbolic Cauchy Problem / by Kunihiko Kajitani, Tatsuo Nishitani.

Format:

Book

Author/Creator:

Kajitani, Kunihiko, 1941- author.

Nishitani, Tatsuo, 1950- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1505.

Lecture Notes in Mathematics, 0075-8434 ; 1505

Language:

English

Subjects (All):

Global analysis (Mathematics).

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource (VIII, 172 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991.

System Details:

text file PDF

Summary:

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.

Other Format:

Printed edition:

ISBN:

9783540466550

Access Restriction:

Restricted for use by site license.