### Author Topic: TT1Problem6  (Read 4167 times)

#### Aida Razi

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##### TT1Problem6
« 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.

#### Levon Avanesyan

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##### Re: TT1Problem6
« Reply #1 on: October 15, 2012, 01:47:38 PM »
I guess yous should apply the method of continuation here.

#### Djirar

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##### Re: TT1Problem6
« Reply #2 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:

$u(x,t) = \frac{1}{ \sqrt{4k \pi t}}\int_{0}^{\infty}{( e^{\frac{-(x-y)^2}{4kt}} - e^{\frac{-(x+y)^2}{4kt}} } )\phi(y) dy$

You can check page 59 of Strauss' book for more details.
« Last Edit: October 15, 2012, 01:56:38 PM by Djirar »

#### Aida Razi

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##### Re: TT1Problem6
« Reply #3 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,

#### Levon Avanesyan

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##### Re: TT1Problem6
« Reply #4 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