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Misc Math / Re: TT1Problem6
« on: October 15, 2012, 01:54:02 PM »
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.
$
\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.