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.
Dans cet article, nous calculons l'indice Gevrey des solutions formelles (avec des conditions initiales données) d'une certaine classe d'équations aux dérivées partielles non linéaires du premier ordre, du type totalement caractéristique et ayant une singularité irrégulière en la variable spatiale. Nous montrons également que l'indice obtenu est génériquement optimal.
Keywords: formal solution, totally characteristic PDF, Gevrey index
Mot clés : solution formelle, PDF totalement caractéristique, indice Gevrey
@article{AIF_2001__51_6_1599_0, author = {Chen, Hua and Luo, Zhuangchu and Tahara, Hidetoshi}, title = {Formal solutions of nonlinear first order totally characteristic type {PDE} with irregular singularity}, journal = {Annales de l'Institut Fourier}, pages = {1599--1620}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {51}, number = {6}, year = {2001}, doi = {10.5802/aif.1867}, mrnumber = {1871282}, zbl = {0993.35003}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1867/} }
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 SP - 1599 EP - 1620 VL - 51 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1867/ DO - 10.5802/aif.1867 LA - en ID - AIF_2001__51_6_1599_0 ER -
%0 Journal Article %A Chen, Hua %A Luo, Zhuangchu %A Tahara, Hidetoshi %T Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity %J Annales de l'Institut Fourier %D 2001 %P 1599-1620 %V 51 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1867/ %R 10.5802/aif.1867 %G en %F AIF_2001__51_6_1599_0
Chen, Hua; Luo, Zhuangchu; Tahara, Hidetoshi. Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity. Annales de l'Institut Fourier, Volume 51 (2001) no. 6, pp. 1599-1620. doi : 10.5802/aif.1867. http://archive.numdam.org/articles/10.5802/aif.1867/
[1] Invariant varieties through singularities of holomorphic vector fields, Annals of Math., Volume 115 (1982) | MR | Zbl
[1] On the holomorphic solution of non-linear totally characteristic equations (To appear in Mathematische Nachrichten, Germany) | Zbl
[2] On totally characteristic type non-linear partial differential equations in the complex domain, Publ. RIMS, Kyoto Univ., Volume 26 (1999), pp. 621-636 | DOI | MR | Zbl
[3] On the holomorphic solution of nonlinear totally characteristic equations with several space variables (Preprint) | Zbl
[4] Nonlinear singular first order partial differential equations of Briot-Bouquet type, Proc. Japan Acad., Volume 66 (1990), pp. 72-74 | DOI | MR | Zbl
[5] Holomorphic and singular solution of nonlinear singular first order partial differential equations, Publ. RIMS, Kyoto Univ., Volume 26 (1990), pp. 979-1000 | DOI | MR | Zbl
[6] Singular nonlinear partial differential equations, Aspects of Mathematics, E 28, Vieweg, 1996 | MR | Zbl
[7] Formal power series solutions of nonlinear first order partial differential equations, Funkcial. Ekvac., Volume 41 (1998), pp. 133-166 | MR | Zbl
[8] Formal solutions with Gevrey type estimates of nonlinear partial differential equations, J. Math. Sci. Univ. Tokyo, Volume 1 (1994), pp. 205-237 | MR | Zbl
[9] Maillet type theorems for nonlinear partial differential equations and the Newton polygons (Preprint) | MR | Zbl
[10] A course of modern analysis, Cambridge Univ. Press, 1958 | MR
[11] Newton polyhedrons and a formal Gevrey space of double indices for linear partial differential operators, Funkcial. Ekvac., Volume 41 (1998), pp. 337-345 | MR | Zbl
Cited by Sources: