Toronto Math Forum

APM346-2016F => APM346--Tests => FE => Topic started by: Victor Ivrii on December 13, 2016, 08:01:10 PM

Title: FE7
Post by: Victor Ivrii 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 $\hat{g}=e^{-|\eta|}$.

Title: Re: FE7
Post by: Sajjan Heerah on December 14, 2016, 09:38:59 AM

My solution attempt to 7

Title: Re: FE7
Post by: brycewu on December 14, 2016, 09:55:21 AM

I got a different answer...

Title: Re: FE7
Post by: Sajjan Heerah 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

Title: Re: FE7
Post by: Sajjan Heerah 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

Title: Re: FE7
Post by: Victor Ivrii on December 18, 2016, 10:11:50 AM

Bruce's solution is correct