# Toronto Math Forum

## APM346-2012 => APM346 Math => Misc Math => Topic started by: Aida Razi on October 15, 2012, 01:33:57 PM

Title: TT1Problem6
Post 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.
Title: Re: TT1Problem6
Post by: Levon Avanesyan on October 15, 2012, 01:47:38 PM
I guess yous should apply the method of continuation here. :)
Title: Re: TT1Problem6
Post by: Djirar 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.
Title: Re: TT1Problem6
Post by: 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?

Thank you guys,
Title: Re: TT1Problem6
Post by: Levon Avanesyan on October 15, 2012, 02:15:11 PM
So, first start with whole interval and then as before examples, make it in the 0<x<+âˆž; Right?
I think so  :)