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

この論文にアクセスする

著者

抄録

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.

収録刊行物

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 56(2), 225-247, 2013

    日本数学会函数方程式論分科会

各種コード

  • NII論文ID(NAID)
    130003363168
  • 本文言語コード
    ENG
  • ISSN
    0532-8721
  • データ提供元
    J-STAGE 
ページトップへ