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

@article{Chen2001FormalSO,
  title={Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity},
  author={Hua Chen and Zhuangchu Luo and Hidetoshi Tahara},
  journal={Annales de l'Institut Fourier},
  year={2001},
  volume={51},
  pages={1599-1620}
}
Dans cet article, nous calculons l'indice Gevrey des solutions formelles (avec des conditions initiales donnees) d'une certaine classe d'equations aux derivees partielles non lineaires du premier ordre, du type totalement caracteristique et ayant une singularite irreguliere en la variable spatiale. Nous montrons egalement que l'indice obtenu est generiquement optimal. 
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References

SHOWING 1-10 OF 10 REFERENCES
On totally characteristic type non-linear partial differential equations in the complex domain
The paper deals with a singular non-linear partial differential equation tdu/dt = F(t, x, u, du/dx) with two independent variables ( t , x ) e C under the assumption that F(t,x,u,v) is holomorphic
Formal solutions with Gevrey type estimates of nonlinear partial differential equations
Abstract. Let L(u) = L(z, ∂αu; |α| ≤ m) be a nonlinear partial differential operator defined in a neighbourhood Ω of z = 0 in Cn+1, where z = (z0, z ′) ∈ C ×Cn. L(u) is a polynomial of the unknown
Singular Nonlinear Partial Differential Equations
Operators with regular singularities. One variable case - Operators with regular singularities. Several variables case - Formal and convergent solutions of singular partial differential equations -
Holomorphic and singular solutions of nonlinear singular first order partial differential equations
In this chapter, we will discuss the following types of non linear singular first order partial differential equations $$t{{\partial u} \over {\partial t}} = F\left( {t,x,u,{{\partial u} \over
A course of modern analysis (4th edition
  • reprinted), Cambridge Univ. Press
  • 1958
WATSON, A course of modern analysis (4th edition, reprinted)
  • 1958