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Math Help - Working with initial and boundary conditions in PDEs

  1. #1
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    Working with initial and boundary conditions in PDEs

    The problem is stated here:
    A homogeneous body occupying the solid region D is completely insulated. Its initial temperature is f(x). Find the steady-state temperature that it reaches after a long time. (Hint: No heat is gained or lost)

    Now, it was asked many months ago:
    Working with initial and boundary conditions in PDEs | MathFax.com

    However, it's no longer on mathhelpforum and the solution there doesn't have the math expressions any more.

    Can any one tell me how to solve it?

    All I have now is:

    du/dn = 0
    u(x, 0) = f(x)
    u_t = k*u_xx

    Intuitively though, I think the solution is a constant.

    please help

    thanks
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  2. #2
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    If steady state then u_t = 0 so u_{xx} = 0 so u = c_1 x + c_2.
    Now you say that at the boundary there's no heat flow so u_x = 0 at the boundaries. Thus

    u_x = c_1 = 0 so u = c_2 is your solution (as you said).
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  3. #3
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    err... Danny

    are you just assuming that the body is 1Dimensional?
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  4. #4
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    I am considering that you gave me

    u_t = k u_{xx}

    and

    u(x,0) = f(x)

    implying a ( 1+1) dimensional problem.
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