The Hyperbolic Cauchy Problem
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"The Hyperbolic Cauchy Problem" by Kunihiko Kajitani, Tatsuo Nishitani is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
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.
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"The Hyperbolic Cauchy Problem" by Kunihiko Kajitani, Tatsuo Nishitani is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Core Mathematics
Author: Kunihiko Kajitani, Tatsuo Nishitani
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
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.
| Author | Kunihiko Kajitani, Tatsuo Nishitani |
| Publisher | Springer |
| Published | 1991 |
| ISBN-13 | 9783540550181 |
| Binding | Paperback |
| Pages | 184 |
| Language | English |
| Subjects | Mathematics |
| Topic | Core Mathematics |
| Series | Lecture Notes in Mathematics |
Format: Paperback
Length: 184 pages
Language: English
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