Characterization of PDE Reducible to ODE under a Certain Homogeneity and Applications to Singular Cauchy Problems

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概要

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• We give a necessary and sufficient condition for a homogeneous partial differential equation in two variables to be reduced to a homogeneous ordinary one under a certain change of variables. It is described by means of the commutator with a first order partial differential operator which characterizes a homogeneity. Moreover we obtain the explicit representation of the reduced ordinary differential equation. This result is a generalization of such a reduction which had been applied to singular Cauchy problems in our previous works [U, WU1]. This fact suggests that local structures of the solutions to partial differential equations can be described by global structures of those to ordinary ones.

• 日本数学会函数方程式論分科会の論文

著者

• Urabe Jiichiroh

  Doshisha University

• Watanabe Takuya

  Ritsumeikan University

関連論文

• Characterization of PDE Reducible to ODE under a Certain Homogeneity and Applications to Singular Cauchy Problems

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