Toronto Math Forum
APM3462012 => APM346 Math => Misc Math => Topic started by: Aida Razi 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.

I guess yous should apply the method of continuation here. :)

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{(xy)^2}{4kt}}  e^{\frac{(x+y)^2}{4kt}} } )\phi(y) dy
\end{equation}
$
You can check page 59 of Strauss' book for more details.

So, first start with whole interval and then as before examples, make it in the 0<x<+âˆž; Right?
Thank you guys,

So, first start with whole interval and then as before examples, make it in the 0<x<+âˆž; Right?
I think so :)