TT1Problem6

[Aida Razi]

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.

[Levon Avanesyan]

I guess yous should apply the method of continuation here.

[Djirar]

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.

[Aida Razi]

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

Thank you guys,

[Levon Avanesyan]

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

I think so