[Sur la sommabilité des solutions formelles de certaines EDP à singularité irrégulière]
Dans la présente Note, nous considérons des classes d'équations aux dérivées partielles, non linéaires et qui sont toutes singulières régulières en t=0 et irrégulières en x=0. Notre but est d'établir un résultat similaire à la k-sommabilité connue pour des équations différentielles méromorphes à points singuliers. Nous montrons que, sous certaines conditions de généricité, toutes les solutions formelles sont Borel sommables ou k-sommables dans toutes les directions du plan des x sauf éventuellement un nombre dénombrable.
In this Note, we consider some classes of nonlinear partial differential equations with regular singularity with respect to t=0 and irregular one with respect to x=0. Our purpose is to establish a result which is similar to the k-summability property, known in the case of singular ordinary differential equations. We can prove that, except at most a countable set, the formal solution is Borel summable or k-summable with respect to x in all other directions.
Publié le :
@article{CRMATH_2003__336_3_219_0,
author = {Luo, Zhuangchu and Chen, Hua and Zhang, Changgui},
title = {On the summability of the formal solutions for some {PDEs} with irregular singularity},
journal = {Comptes Rendus. Math\'ematique},
pages = {219--224},
publisher = {Elsevier},
volume = {336},
number = {3},
year = {2003},
doi = {10.1016/S1631-073X(03)00023-2},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00023-2/}
}
TY - JOUR AU - Luo, Zhuangchu AU - Chen, Hua AU - Zhang, Changgui TI - On the summability of the formal solutions for some PDEs with irregular singularity JO - Comptes Rendus. Mathématique PY - 2003 SP - 219 EP - 224 VL - 336 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00023-2/ DO - 10.1016/S1631-073X(03)00023-2 LA - en ID - CRMATH_2003__336_3_219_0 ER -
%0 Journal Article %A Luo, Zhuangchu %A Chen, Hua %A Zhang, Changgui %T On the summability of the formal solutions for some PDEs with irregular singularity %J Comptes Rendus. Mathématique %D 2003 %P 219-224 %V 336 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00023-2/ %R 10.1016/S1631-073X(03)00023-2 %G en %F CRMATH_2003__336_3_219_0
Luo, Zhuangchu; Chen, Hua; Zhang, Changgui. On the summability of the formal solutions for some PDEs with irregular singularity. Comptes Rendus. Mathématique, Tome 336 (2003) no. 3, pp. 219-224. doi : 10.1016/S1631-073X(03)00023-2. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00023-2/
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