1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook