Bulletin of the Faculty of Education, Yamaguchi University. Natural science

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Bulletin of the Faculty of Education, Yamaguchi University. Natural science Volume 15 Issue 2
published_at 1966-03

An Application of Fourier Integral.

Fourier二重積分の一つの応用
Tamura Toshio
About This Article
Descriptions
Fourierの二重積分の一つの応用として一つの二階偏微分方程式の解法を試みる。Fourierの二重積分とはf(x)が-∞<x<∞でDirichletの条件に適し∫^∞|f(x)|dxが存在するとき∫^∞_<dα>∫^∞f(ξ)cosα(ξ-x)dξ=π/2{f(-0)+f(-0)}が成立する。特にf(x)がxで連続ならf(x)=1/π∫^∞_0dα∫^∞_<-∞>fξ)cosα(ξ-x)dξとなる。今(∂z)/(∂y)=k^2(∂^2z)/(∂y^2)k)0, y>0………(1)z=f(x)の解を求めてみる。z=e^<βy>(Acosχχ+Bsinαχ)A,B,α,β……定数とおいてみると(∂z)/(∂y)=β〓^<3γ>(Acosχχ+Esinχχ)(∂^2z)/(∂x^2)=-α^2e^<3γ>(Acosαχ+Bsinαχ)
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