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Heat (or diffusion) equation in semi infinite region

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations

    [tex]
    \[
    \frac{{\partial c\left( {x,t} \right)}}{{\partial t}} = D\frac{{\partial ^2 c\left( {x,t} \right)}}{{\partial ^2 x}}
    \]
    [/tex]

    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:
    [tex]
    \[
    \left\{ \begin{array}{l}
    c\left( {x,0} \right) = \delta \left( {x - x_0 } \right) \\
    c_x \left( {0,t} \right) = 0 \\
    \end{array} \right.
    \]
    [/tex]
    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.
     
  2. jcsd
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