The Hyperbolic Cauchy Problem
Kajitani, Kunihiko.
The Hyperbolic Cauchy Problem [electronic resource] / by Kunihiko Kajitani, Tatsuo Nishitani. - VIII, 172 p. online resource. - Lecture Notes in Mathematics, 1505 0075-8434 ; . - Lecture Notes in Mathematics, 1505 .
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.
9783540466550
10.1007/BFb0090882 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515
The Hyperbolic Cauchy Problem [electronic resource] / by Kunihiko Kajitani, Tatsuo Nishitani. - VIII, 172 p. online resource. - Lecture Notes in Mathematics, 1505 0075-8434 ; . - Lecture Notes in Mathematics, 1505 .
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.
9783540466550
10.1007/BFb0090882 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515