maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. part ii

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ID: 160154
2015
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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.
Reference Key
shirai2015opusculamaillet Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Akira Shirai
Journal zhonghua yi xue za zhi
Year 2015
DOI
http://dx.doi.org/10.7494/OpMath.2015.35.5.689
URL
http://www.opuscula.agh.edu.pl/vol35/5/art/opuscula_math_3537.pdf
Keywords
quantitative methods

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