The Hyperbolic Cauchy Problem

The approach to the Cauchy problem taken here by the authorsis based on theuse of Fourier integral operators with acomplex-valued phase function, which is a time functionchosen suitably according to the geometry of the multiplecharacteristics. The correctness of the Cauchy problem inthe Gevrey classes for operators with hyperbolic principalpart is shown in the first part. In the second part, thecorrectness of the Cauchy problem for effectively hyperbolicoperators is proved with a precise estimate of the loss ofderivatives. This method can be applied to other (non)hyperbolic problems. The text is based on a course oflectures given for graduate students but will be of interestto researchers interested in hyperbolic partial differentialequations. In the latter part the reader is expected to befamiliar with some theory of pseudo-differential operators.

List of contents

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

Product details

• Authors: Kunihiko Kajitani, Tatsuo Nishitani
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 25.06.2009
• EAN: 9783540550181
• ISBN: 978-3-540-55018-1
• No. of pages: 172
• Dimensions: 157 mm x 237 mm x 11 mm
• Weight: 281 g
• Illustrations: VIII, 172 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics, Volume 1505; Lecture Notes in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis