Hyperbolic Cauchy problem and Leray's residue formula

Susumu Tanabé

Annales Polonici Mathematici (2000)

  • Volume: 74, Issue: 1, page 275-290
  • ISSN: 0066-2216

Abstract

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We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.

How to cite

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Tanabé, Susumu. "Hyperbolic Cauchy problem and Leray's residue formula." Annales Polonici Mathematici 74.1 (2000): 275-290. <http://eudml.org/doc/208371>.

@article{Tanabé2000,
abstract = {We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.},
author = {Tanabé, Susumu},
journal = {Annales Polonici Mathematici},
keywords = {Leray's residue formula; Gauss-Manin connexion; Bonn; hyperbolic Cauchy problem; asymptotic expansion; Gauss-Nanin systems},
language = {eng},
number = {1},
pages = {275-290},
title = {Hyperbolic Cauchy problem and Leray's residue formula},
url = {http://eudml.org/doc/208371},
volume = {74},
year = {2000},
}

TY - JOUR
AU - Tanabé, Susumu
TI - Hyperbolic Cauchy problem and Leray's residue formula
JO - Annales Polonici Mathematici
PY - 2000
VL - 74
IS - 1
SP - 275
EP - 290
AB - We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.
LA - eng
KW - Leray's residue formula; Gauss-Manin connexion; Bonn; hyperbolic Cauchy problem; asymptotic expansion; Gauss-Nanin systems
UR - http://eudml.org/doc/208371
ER -

References

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  17. [17] S. Tanabé, Connexion de Gauss-Manin associée à la déformation verselle des singularités isolées d'hypersurface et son application au XVIe problème de Hilbert, preprint. 
  18. [18] S. Tanabé, On geometry of fronts in wave propagations, in: Geometry and Topology of Caustics-Caustics'98, Banach Center Publ. 50, Inst. Math., Polish Acad. Sci., 1999, 287-304. Zbl0951.35074
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