It is known that the formal solution to an equation of non-Kowalevski type is divergent in general. To this divergent solution it is important to evaluate the rate of divergence or the Gevrey order, and such a result is often called a Maillet type theorem. In this paper the Maillet type theorem is proved for divergent solutions to singular partial differential equations of non-Kowalevski type, and it is shown that the Gevrey order is characterized by a Newton polygon associated with an equation. In order to prove our results the majorant method is effectively employed.
Publié le : 2001-07-15
Classification:
singular PDE,
divergent solution,
Gevrey order,
Newton polygon,
35A07,
35A20,
35C10
@article{1213023724,
author = {SHIRAI, Akira},
title = {Maillet type theorem for nonlinear partial differential equations and Newton polygons},
journal = {J. Math. Soc. Japan},
volume = {53},
number = {3},
year = {2001},
pages = { 565-587},
language = {en},
url = {http://dml.mathdoc.fr/item/1213023724}
}
SHIRAI, Akira. Maillet type theorem for nonlinear partial differential equations and Newton polygons. J. Math. Soc. Japan, Tome 53 (2001) no. 3, pp. 565-587. http://gdmltest.u-ga.fr/item/1213023724/