- #1
CGandC
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Homework Statement
Solve the following partial differential equation , using Fourier Transform:
Given the following:
And a initial condition:
Homework Equations
The Attempt at a Solution
First , i associate spectral variables to the x and t variables:
## k ## is the spectral variable corresponding to ## x ##
## \omega ## is the spectral variable corresponding to ## t ##
Using Fourier transform on the PDE , i get:
## (i\omega)(ik)\widetilde{u(\omega,k)}=(ik)^2 \widetilde{u(\omega,k)} ##
After simplifying , I get : ## \omega = k ##
How am I supposed to proceed from here? ( I didn't find ## \widetilde{u(\omega,k)} ## )