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Diffusion equation in 2d

  1. Oct 23, 2010 #1
    Show that S2 = S(x,t)S(y,t) solves St = k (Sxx + Syy)

    well
    St = St(x,t)S(y,t) + S(x,t)St(y,t)
    Sxx = Sxx(x,t)S(y,t)
    Syy=Syy(y,t)S(x,t)

    but what do i do from there?
     
  2. jcsd
  3. Oct 23, 2010 #2

    fzero

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    Presumably S(x,t) is the solution to a closely related equation?
     
  4. Oct 23, 2010 #3
    Well yeah, I thought about assuming that S(x,t) and S(y,t) solve the 1d diffusion equation in their respective dimensions, and then it's easy to just replace all the Sts with the Sxx and Syys, but the question doesn't provide any assumptions about S(x,t) and S(y,t) being solutions to the 1d equation. Is that just something I should assume anyway?
     
  5. Oct 23, 2010 #4

    fzero

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    If you divide through by S(x,t)S(y,t) you will be able to find the equation that S(x,t) must satisfy. It's not quite the 1d diffusion equation, but it looks easy to solve.
     
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