1. Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II
- Author
-
Akira Shirai
- Subjects
formal solution ,Partial differential equation ,Formal power series ,Maillet type theorem ,General Mathematics ,lcsh:T57-57.97 ,Mathematical analysis ,First-order partial differential equation ,Mathematics::Analysis of PDEs ,Order (ring theory) ,Type (model theory) ,Nonlinear system ,Convergence (routing) ,lcsh:Applied mathematics. Quantitative methods ,singular partial differential equations ,Divergence (statistics) ,totally characteristic type ,Mathematics ,nilpotent vector field ,Gevrey order - 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.
- Published
- 2015