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Math Help - BVP

  1. #1
    ux0
    ux0 is offline
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    BVP

    For what constant value of q does the boundary value problem

    u_t=u_{xx} + q . . . 0<x<2, t>0
    u_x(0,t)=2 . . . . . t \geq 0
    u_x(2,t)=0 . . . . . t \geq 0
    u(x,o)=f(x) . . . . . 0 \leq x \leq 2

    have a steady state solution? Find the complete solution when

    <br />
f(x)=\left\{\begin{matrix}<br />
2x \mapsto 0 \leq x \leq 1<br />
\\ <br />
x \mapsto 1 \leq x \leq 2<br />
\end{matrix}\right.




    So to find the steady state solution i did the following steps. (The notation i use is the notation we use in class)

    0=U''+q \Rightarrow  U''=-q

    U'(x)=-qx + A

    U(x)= \frac{-q}{2}x^2 + Ax + B

    using my endpoint conditions i get

    U'(2) = 0 = -q2 + A

    A=2q

    U'(0)=2=2q \rightarrow 1=q \rightarrow A=2

    So my steady state solution is

    U(x)=\frac{-1}{2}x^2+2x+B

    which is only valid when q = 1... If this part is right, I can't seem to find the complete solution when i have the Constant B...
    Last edited by ux0; October 29th 2009 at 05:54 PM.
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  2. #2
    Super Member Rebesques's Avatar
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    Take B=0, and it is a steady state solution.
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