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

1. Feb 6, 2012

### Mugged

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 = $\xi$(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. Feb 6, 2012

### Mugged

nevermind, i have figured out the problem

thanks