Use the Fourier transform method to show that the transform solution of the(n+1)-dimensional, inhomogeneous, Klein-Gordon equationu+d'u=q(x,t), reR", 1>0,axwith the Cauchy datandimu(x,0) = f(x) and ,(x,0)= g(x) for all r e R"isU(k.1) = F(k)cos tye"|& f+d +G(k)%3DQ(k, t-t) dr,where U (k,t) =F{u(x,t)}, *3=(x,,x.) and k =%3Duotion in

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Answered: Use the Fourier transform method to…

Use the Fourier transform method to show that the transform solution of the (n+1)-dimensional, inhomogeneous, Klein-Gordon equation

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question

Use the Fourier transform method to show that the transform solution of the
(n+1)-dimensional, inhomogeneous, Klein-Gordon equation
u+d'u=q(x,t), reR", 1>0,
ax
with the Cauchy data
ndim
u(x,0) = f(x) and ,(x,0)= g(x) for all r e R"
is
U(k.1) = F(k)cos tye"|& f+d +
G(k)
%3D
Q(k, t-t) dr,
where U (k,t) =F{u(x,t)}, *3=
(x,,x.) and k =
%3D
uotion in

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