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Intro to PDE: Related homogeneous boundary condtions

  1. Apr 22, 2008 #1
    (partial derivatives didn't carry over well, so I just used a d)

    1. The problem statement, all variables and given/known data
    Give an example (as simple as possible) of a reference temperature distribution r = r(x, t) satisfying the following boundary conditions

    DN: r(0, t) = A(t), (dr(L,t) / dx) = B(t);
    NN: (dr(0,t) / dx) = A(t); (dr(L,t) / dx )= B(t);

    For each of the above BC, compute the reference source function:

    Qr(x, t) =dr / dt−d(^2)r / dx(^2) .


    2. Relevant equations

    I don't know if these are actually relevant.

    v(x,t) = u(x,t) - r(x,t)
    dv/dt = d(^2)v / dx(^2) + [Q(x,t) - dr / dt + d(^2)r / dt + d(^2)r / dx(^2)


    3. The attempt at a solution

    I basically just solved r for the boundary conditions then took the derivatives with respect to t and x to find Qr(x,t), but I don't know if that's right. My answer for the DN case of Qr ended up as : dA / dt + ( dB / dt )*x

    Are solutions like that okay, or am I supposed to be doing something else?
     
  2. jcsd
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