# Heat (or diffusion) equation in semi infinite region

1. Feb 21, 2010

### shultz

1. The problem statement, all variables and given/known data
2. Relevant equations

$$$\frac{{\partial c\left( {x,t} \right)}}{{\partial t}} = D\frac{{\partial ^2 c\left( {x,t} \right)}}{{\partial ^2 x}}$$$

3. The attempt at a solution

First of all, I am not sure how to translate the given data to exact mathematical boundary conditions.
Are the boundary condition in part a are:
$$$\left\{ \begin{array}{l} c\left( {x,0} \right) = \delta \left( {x - x_0 } \right) \\ c_x \left( {0,t} \right) = 0 \\ \end{array} \right.$$$
If it is correct, how do I continue from here?
I know I can solve the equation for infinite region (from both sides) using Fourier transform but I am not sure how to do it on semi infinite region using the given clue.

Thanks a lot!

P.S. I am new to this forum and I am not sure where to put this question (math homework, physics homework, maybe math differential equations etc.) so please forgive me and transfer the question to its more appropriate place.