TY  - JOUR
ID  - Shirai2015
LB  - Shirai2015
AU  - Shirai, Akira
TI  - Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II
ST  - Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 5
SP  - 689
EP  - 712
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.5.689
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.5.689
AB  - 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.
KW  - singular partial differential equations
KW  - totally characteristic type
KW  - nilpotent vector field
KW  - formal solution
KW  - Gevrey order
KW  - Maillet type theorem
SN  - 1232-9274
ER  -