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.

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.

DOI: 10.5802/aif.1867
Classification: 35A07,  35A10,  35A20
Keywords: formal solution, totally characteristic PDF, Gevrey index
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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     title = {Formal solutions of nonlinear first order totally characteristic type {PDE} with irregular singularity},
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     pages = {1599--1620},
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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, Volume 51 (2001) no. 6, pp. 1599-1620. doi : 10.5802/aif.1867. http://archive.numdam.org/articles/10.5802/aif.1867/

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