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One-Dimensional Heat Equation Problem

  1. Jun 14, 2009 #1
    Hi, I need help to solve this problem, about 1-D heat equation

    [tex]\partial[/tex]u / [tex]\partial[/tex]t = k ([tex]\partial[/tex]2u / [tex]\partial[/tex]x2)-2u (0< x <1)

    u(x,0)=e-x
    u(0,t)=e-2t
    u(1,t)=0

    I need to solve it with separation variable
     
  2. jcsd
  3. Jun 14, 2009 #2

    Office_Shredder

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    Ok... what have you done so far? Do you know how to start a problem like this?
     
  4. Jun 14, 2009 #3
    No, I have no idea how to start it, bcos it's non-homogeneous eq, can u help me?
     
  5. Jun 15, 2009 #4

    Office_Shredder

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    I just realized that you don't actually have the heat equation in your first post. There should be no -2u term in the equation. Can you verify what you're supposed to be solving?

    If you're actually trying to solve the heat equation, then start with u(x,t) = X(x)T(t) for some X and T functions and then try to separate the x's and the t's
     
  6. Jun 15, 2009 #5

    HallsofIvy

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    Even with the "-2u" term, do exactly what Office Shredder says, just what you would normally do to "separate variables"- let u(x,t)= X(x)T(t) and put into the equation:

    [tex]X\frac{du}{dt}= \kappa T\frac{d^2X}{dx^2}- 2XT[/tex]

    divided through by XT and see what happens.
     
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