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APM346-2012
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TT1Problem6
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Topic: TT1Problem6 (Read 5810 times)
Aida Razi
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Posts: 62
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TT1Problem6
«
on:
October 15, 2012, 01:33:57 PM »
In past term test 1, problem 6:
Write the solution of the diffusion equation on a half line 0<x<+âˆž,
I was wondering if we need to calculate integral on just 0<x<+âˆž interval and not whole interval.
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Levon Avanesyan
Full Member
Posts: 21
Karma: 1
Re: TT1Problem6
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Reply #1 on:
October 15, 2012, 01:47:38 PM »
I guess yous should apply the method of continuation here.
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Djirar
Full Member
Posts: 24
Karma: 8
Re: TT1Problem6
«
Reply #2 on:
October 15, 2012, 01:54:02 PM »
This is a reflection problem with Dirichlet boundary condition. The solution on the interval 0<x< âˆž is given by:
$
\begin{equation}
u(x,t) = \frac{1}{ \sqrt{4k \pi t}}\int_{0}^{\infty}{( e^{\frac{-(x-y)^2}{4kt}} - e^{\frac{-(x+y)^2}{4kt}} } )\phi(y) dy
\end{equation}
$
You can check page 59 of Strauss' book for more details.
«
Last Edit: October 15, 2012, 01:56:38 PM by Djirar
»
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Aida Razi
Sr. Member
Posts: 62
Karma: 15
Re: TT1Problem6
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Reply #3 on:
October 15, 2012, 02:11:53 PM »
So, first start with whole interval and then as before examples, make it in the 0<x<+âˆž; Right?
Thank you guys,
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Levon Avanesyan
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Re: TT1Problem6
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Reply #4 on:
October 15, 2012, 02:15:11 PM »
Quote from: Aida Razi on October 15, 2012, 02:11:53 PM
So, first start with whole interval and then as before examples, make it in the 0<x<+âˆž; Right?
I think so
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