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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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  2. [2] P. Appel et J. Kampé de Fériet, Fonctions hypergéometriques et hypersphériques, Gauthier-Villars, Paris, 1926. 
  3. [3] E. Brieskorn, Die Monodromie der isolierten Singularitäten von Hyperflächen, Manuscripta Math. 2 (1970), 103-161. Zbl0186.26101
  4. [4] L. Gårding, Sharp fronts of paired oscillatory integrals, Publ. RIMS Kyoto Univ. 12 suppl. (1977), 53-68. 
  5. [5] G.-M. Greuel, Der Gauß-Manin Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214 (1975), 235-266. Zbl0285.14002
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  9. [9] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I, Springer, 1984. 
  10. [10] E. Leichtnam, Le problème de Cauchy ramifié linéaire pour des données à singularités algébriques, Mem. Soc. Math. France 53 (1993). Zbl0819.35007
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  14. [14] F. Pham, Introduction à l'étude topologique des singularités de Landau, Gauthier-Villars, 1967. 
  15. [15] S. Tanabé, Lagrangian variety and the condition for the presence of sharp front of the fundamental solution to Cauchy problem, Sci. Papers College Arts Sci. Univ. Tokyo, 42 (1992), 149-159. Zbl0802.35092
  16. [16] S. Tanabé, Transformée de Mellin des intégrales fibres de courbe espace associées aux singularités isolées d'intersection complète quasihomogènes, Compositio Math., to appear. 
  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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  20. [20] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293. Zbl0813.47060

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