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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< 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.

$

\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.