Author Topic: FE7  (Read 224 times)

Victor Ivrii

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FE7
« on: December 13, 2016, 08:01:10 PM »
Solve using (partial) Fourier transform with respect to $y$
\begin{align}
&\Delta u:=u_{xx}+u_{yy}=0, &&x>0,\label{7-1}\\
&u|_{x=0}= g(y),\label{7-2}\\
&\max |u|<\infty\label{7-3}
\end{align}
with $g(y)=\frac{2}{y^2+1}$.

Hint. Fourier transform of $g(y)$ is $\hat{g}=e^{-|\eta|}$.

Sajjan Heerah

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Re: FE7
« Reply #1 on: December 14, 2016, 09:38:59 AM »
My solution attempt to 7

brycewu

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Re: FE7
« Reply #2 on: December 14, 2016, 09:55:21 AM »
I got a different answer...

Sajjan Heerah

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Re: FE7
« Reply #3 on: December 14, 2016, 10:08:41 AM »
I'm pretty sure I made a sign error and I have an extra 1/sqrt(2pi) factor

Sajjan Heerah

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Re: FE7
« Reply #4 on: December 14, 2016, 10:21:18 AM »
I think my error was that I missed that there should be an absolute value on the frequency term when you solve the transformed problem, guess that means I did this wrong on the exam
« Last Edit: December 14, 2016, 10:29:21 AM by Sajjan Heerah »

Victor Ivrii

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Re: FE7
« Reply #5 on: December 18, 2016, 10:11:50 AM »
Bruce's solution is correct