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Book 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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: The Hyperbolic Cauchy Problem
• Author: Kunihiko Kajitani, Tatsuo Nishitani
• Language: English
• Binding: Paperback
• Number of pages: 172
• EAN: 9783540550181
• ISBN: 3540550186
• ID: 01565495
• Publisher: Springer, Berlin
• Weight: 281 g
• Dimensions: 237 × 157 × 11 mm
• Published: 2008

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