Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II

Opuscula Mathematica

Akira Shirai¹ 

[1] Sugiyama Jogakuen University, School of Education, Department of Child Development, 17-3 Hoshigaoka Motomachi, Chikusa, Nagoya, 464-8662, Japan;

关键词: singular partial differential equations;    totally characteristic type;    nilpotent vector field;    formal solution;    Gevrey order;    Maillet type theorem;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2015.35.5.689

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown