Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity

Hua Chen[1]; Zhuangchu Luo[2]; Hidetoshi Tahara

  • [1] Wuhan University, Institute of Mathematics, Wuhan (Rép. Pop. Chine)
  • [2] Sophia University, Department of Mathematics, Tokyo (Japon)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 6, page 1599-1620
  • ISSN: 0373-0956

Abstract

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In this paper, we calculate the formal Gevrey index of the formal solution of a class of nonlinear first order totally characteristic type partial differential equations with irregular singularity in the space variable. We also prove that our index is the best possible one in a generic case.

How to cite

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Chen, Hua, Luo, Zhuangchu, and Tahara, Hidetoshi. "Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity." Annales de l’institut Fourier 51.6 (2001): 1599-1620. <http://eudml.org/doc/115960>.

@article{Chen2001,
abstract = {In this paper, we calculate the formal Gevrey index of the formal solution of a class of nonlinear first order totally characteristic type partial differential equations with irregular singularity in the space variable. We also prove that our index is the best possible one in a generic case.},
affiliation = {Wuhan University, Institute of Mathematics, Wuhan (Rép. Pop. Chine); Sophia University, Department of Mathematics, Tokyo (Japon)},
author = {Chen, Hua, Luo, Zhuangchu, Tahara, Hidetoshi},
journal = {Annales de l’institut Fourier},
keywords = {formal solution; totally characteristic PDF; Gevrey index; formal Gevrey class},
language = {eng},
number = {6},
pages = {1599-1620},
publisher = {Association des Annales de l'Institut Fourier},
title = {Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity},
url = {http://eudml.org/doc/115960},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Chen, Hua
AU - Luo, Zhuangchu
AU - Tahara, Hidetoshi
TI - Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 6
SP - 1599
EP - 1620
AB - In this paper, we calculate the formal Gevrey index of the formal solution of a class of nonlinear first order totally characteristic type partial differential equations with irregular singularity in the space variable. We also prove that our index is the best possible one in a generic case.
LA - eng
KW - formal solution; totally characteristic PDF; Gevrey index; formal Gevrey class
UR - http://eudml.org/doc/115960
ER -

References

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  1. C. Camacho, P. Sad, Invariant varieties through singularities of holomorphic vector fields, Annals of Math. 115 (1982) Zbl0503.32007MR657239
  2. H. Chen, H. Tahara, On the holomorphic solution of non-linear totally characteristic equations Zbl1017.35006
  3. H. Chen, H. Tahara, On totally characteristic type non-linear partial differential equations in the complex domain, Publ. RIMS, Kyoto Univ. 26 (1999), 621-636 Zbl0961.35002MR1719863
  4. H. Chen, Z. Luo, On the holomorphic solution of nonlinear totally characteristic equations with several space variables Zbl1003.35005
  5. R. Gérard, H. Tahara, Nonlinear singular first order partial differential equations of Briot-Bouquet type, Proc. Japan Acad. 66 (1990), 72-74 Zbl0711.35034MR1051596
  6. R. Gérard, H. Tahara, Holomorphic and singular solution of nonlinear singular first order partial differential equations, Publ. RIMS, Kyoto Univ. 26 (1990), 979-1000 Zbl0736.35022MR1079905
  7. R. Gérard, H. Tahara, Singular nonlinear partial differential equations, E 28 (1996), Vieweg Zbl0874.35001MR1757086
  8. R. Gérard, H. Tahara, Formal power series solutions of nonlinear first order partial differential equations, Funkcial. Ekvac. 41 (1998), 133-166 Zbl1142.35310MR1627341
  9. S. Ouchi, Formal solutions with Gevrey type estimates of nonlinear partial differential equations, J. Math. Sci. Univ. Tokyo 1 (1994), 205-237 Zbl0810.35006MR1298544
  10. A. Shirai, Maillet type theorems for nonlinear partial differential equations and the Newton polygons Zbl0995.35002MR1828970
  11. E. T. Whittaker, G. N. Watson, A course of modern analysis, (1958), Cambridge Univ. Press Zbl45.0433.02MR1424469
  12. H. Yamazawa, Newton polyhedrons and a formal Gevrey space of double indices for linear partial differential operators, Funkcial. Ekvac. 41 (1998), 337-345 Zbl1140.35575MR1676878

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