Toronto Math Forum
APM346-2012 => APM346 Math => Misc Math => Topic started by: Aida Razi on October 15, 2012, 01:33:57 PM
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In past term test 1, problem 6:
Write the solution of the diffusion equation on a half line 0<x<+∞,
I was wondering if we need to calculate integral on just 0<x<+∞ interval and not whole interval.
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I guess yous should apply the method of continuation here. :)
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This is a reflection problem with Dirichlet boundary condition. The solution on the interval 0<x< ∞ 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.
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So, first start with whole interval and then as before examples, make it in the 0<x<+∞; Right?
Thank you guys,
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So, first start with whole interval and then as before examples, make it in the 0<x<+∞; Right?
I think so :)