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Homework Help: Very weird PDE problem

  1. Sep 30, 2007 #1


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    The question is:

    Write a short paragraph that physical problem modeled by the equation:

    \frac{\partial{U}}{\partial{t}} = \frac{1}{4}\frac{\partial^2{U}}{\partial^2{x}} -12[U - 8x][/tex]

    Subject to
    IC: U(x,0) = 3x
    BCs: U(0,t) =0, u(2,t) = 2t

    Okay so clearly, the physical problem is some kind of heat problem with a one dimensional rod and a heat source term. However, the problem is that the IC and the BCs are conflicting, since U(2,0) = 6, from the IC, but U(2,0) = 0 from the BC. Any advice to go about answering this?
  2. jcsd
  3. Oct 3, 2007 #2


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    What that means is that your function is not continuous. That's alright if you are using integration techniques which will "smooth" the discontinuity. I would recommend using a Fourier series solution. In fact, I would write V(x,t)= U(x,t)- 2t and solve the problme for V so that the boundary conditions are "homogeneous" and you can use a Fourier sine series.
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