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Thread: Applying boundary conditions to heat equation

  1. #1
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    Question Applying boundary conditions to heat equation

    I follow the course for solving the heat equation. However, I cannot understand a possible case of semi-infinite.

    The solution is

    $$\phi(x) = c_1\cos (\sqrt{\lambda}x) + c_2 \sin(\sqrt{\lambda} x)$$


    as we have to obtain $\lambda$ by applying the boundary conditions. All example are for $x=0$ and $x=L$. I am trying to figure out how to solve it for a simple set of boundary conditions:

    $$u(x,t)=0, u(0,t)=10, u(\infty,t)=0$$

    How do we apply $\phi(\infty) = 0$ to obtain $\lambda$?
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  2. #2
    MHF Contributor

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    Re: Applying boundary conditions to heat equation

    Set the problem up for some fixed "L" and then take the limit as L goes to infinity.
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