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Solving a PDE and finding the jump condition (method of characteristics)

  1. Feb 6, 2012 #1
    Here I have my PDE:

    http://desmond.imageshack.us/Himg718/scaled.php?server=718&filename=pde.png&res=medium [Broken]

    I have found the solution by using the method of characteristics two times, one for x<0 and the other for x>0.

    I have: U(x,y) = o for x<0 and U(x,y) = Uo(x-1)/(1+Uo*y) for x>0

    The trouble im having is finding the jump curve, x = [itex]\xi[/itex](y),

    Im not sure if im doing this correctly, but I keep getting the natural log of something, while my book says the correct answer is 1 - sqrt(1+Uo*y) for the jump curve...

    can anyone help me?

    much appreciated
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Feb 6, 2012 #2
    nevermind, i have figured out the problem

    thanks
     
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