The Hyperbolic Cauchy Problem

1991
ISBN: 978-3-540-55018-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1505, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Nishitani, Tatsuo

Kajitani, Kunihiko

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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