Opuscula Mathematica
Opuscula Math. 35, no. 5 (), 689-712
http://dx.doi.org/10.7494/OpMath.2015.35.5.689
Opuscula Mathematica

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


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.
Mathematics Subject Classification: 35F20, 35A20, 35C10.
Cite this article as:
Akira Shirai, Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II, Opuscula Math. 35, no. 5 (2015), 689-712, http://dx.doi.org/10.7494/OpMath.2015.35.5.689
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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