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Riemann function for a second order hyperbolic PDE

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the Riemann function for

    uxy + xyux = 0, in x + y > 0
    u = x, uy = 0, on x+y = 0

    2. Relevant equations



    3. The attempt at a solution

    I think the Riemann function, R(x,y;s,n), must satisfy:

    0 = Rxy - (xyR)x
    Rx = 0 on y =n
    Ry = xyR on x = s
    R = 1 at (x,y) = (s,n)

    But I don't know how to solve this beyond just spotting a solution.
     
  2. jcsd
  3. Feb 27, 2012 #2

    I like Serena

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    Homework Helper

    How about:
    0 = Rxy - (xyR)x
    g(y) = Ry - xyR

    Pick g(y)=0, just to find a particular solution.
    Ry = xyR
    Ry/R = xy
    ln R = xy2/2 + h(x)
    R=exp(xy2/2) H(x)
     
  4. Feb 27, 2012 #3
    Thanks :)
     
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