@Article{Shirai2015,
author = "Shirai, Akira",
title = "Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II",
journal = "Opuscula Math.",
year = "2015",
volume = "35",
number = "5",
pages = "689--712",
doi = "http://dx.doi.org/10.7494/OpMath.2015.35.5.689",
url = "http://dx.doi.org/10.7494/OpMath.2015.35.5.689",
abstract = "In this paper, we study the following nonlinear first order partial differential equation: \[f(t,x,u,\partial_t u,\partial_x u)=0\quad\text{with}\quad u(0,x)\equiv 0.\] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002), 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005), 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.",
keywords = "singular partial differential equations, totally characteristic type, nilpotent vector field, formal solution, Gevrey order, Maillet type theorem",
issn = "1232-9274"
}