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Diffusion equation, boundary conditions

  1. Oct 1, 2011 #1
    EDIT: The subscripts in this question should all be superscripts!

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

    I'm trying to solve a temperature problem involving the diffusion equation, which has led me to the expression:

    X(x) = Cekx+De-kx

    Where U(x,y) = X(x)Y(y)
    and I am ignoring any expressions where Y(y)=0 or X(x)=0 for all values of their variables as these are trivial solutions.

    I'm told I can simplify things by applying one of the boundary conditions:

    As x tends towards infinity, U(x,y) tends towards 0.


    2. Relevant equations



    3. The attempt at a solution

    So my question is, how do I apply this to the general solution I've found for X(x)?
    I know that Y(y) is not zero, so I effectively have X(x) going to zero as x tends towards infinity. So I need to work out what happens to Cekx + De-kx. As 1/x tends to 0 as x tends to infinity, can I assume that D/ekx also tends towards 0? Or does it tend to D? And what about C?

    Thank in advance for any help
     
    Last edited: Oct 1, 2011
  2. jcsd
  3. Oct 1, 2011 #2
    Is this your equation...?

    [tex]X(x) = Ce^{kx} + De^{-kx}[/tex]
     
  4. Oct 2, 2011 #3
    Yes, that's right.

    I've worked out that C=0 as this is the only way to ensure X(x)=0 as x tends to infinity.

    Thanks anyway
     
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