Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity
[Solutions formelles d'équations aux dérivées partielles non linéaires du premier ordre, de type totalement caractéristique]
Chen, Hua1 ; Luo, Zhuangchu2 ; Tahara, Hidetoshi
1 Wuhan University, Institute of Mathematics, Wuhan (Rép. Pop. Chine)
2 Sophia University, Department of Mathematics, Tokyo (Japon)
Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1599-1620.

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.

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.

DOI : 10.5802/aif.1867
Classification : 35A07, 35A10, 35A20
Keywords: formal solution, totally characteristic PDF, Gevrey index
Mot clés : solution formelle, PDF totalement caractéristique, indice Gevrey
Chen, Hua 1 ; Luo, Zhuangchu 2 ; Tahara, Hidetoshi 

1 Wuhan University, Institute of Mathematics, Wuhan (Rép. Pop. Chine)
2 Sophia University, Department of Mathematics, Tokyo (Japon) 
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     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},
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Chen, Hua; Luo, Zhuangchu; Tahara, Hidetoshi. Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity. Annales de l'Institut Fourier, Tome 51 (2001) no. 6, pp. 1599-1620. doi : 10.5802/aif.1867. http://www.numdam.org/articles/10.5802/aif.1867/

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