The Hyperbolic Cauchy Problem

Kunihiko Kajitani, Tatsuo Nishitani (Autoren)

Buch | Softcover

VIII, 172 Seiten

1991
Springer Berlin (Verlag)
978-3-540-55018-1 (ISBN)

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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.

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

Erscheint lt. Verlag	13.12.1991
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VIII, 172 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	281 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Cauchy problem • Derivative • differential equation • hyperbolic operators • hyperbolic partial differential equation • partial differential equation • Partial differential equations • phase function • pseudo-differential operators
ISBN-10	3-540-55018-6 / 3540550186
ISBN-13	978-3-540-55018-1 / 9783540550181
Zustand	Neuware