1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted