Overview

The approach to the Cauchy problem taken here by the authors is based on the use 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 section of the text. In the second section, the correctness of the Cauchy problem for effectively hyperbolic operators is proved with a precise estimate of the loss 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 the theory of pseudo-differential operators.

Full Product Details

Author:   Kunihiko Kajitani ,  Tatsuo Nishitani
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1991 ed.
Volume:   1505
Dimensions:   Width: 15.50cm , Height: 0.90cm , Length: 23.50cm
Weight:   0.580kg
ISBN:  

9783540550181

ISBN 10:   3540550186
Pages:   172
Publication Date:   13 December 1991
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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

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