1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

PDE question.

  1. Dec 31, 2013 #1
    1. The problem statement, all variables and given/known data
    I have solved ux + (x/y)uy = 0 using characteristics, to obtain
    u(x,y)=C (for y=+-x) and f(x2-y2)

    2. Relevant equations

    3. The attempt at a solution
    I was then given two boundary conditions:
    (a) u(x=0,y)=cos(y), which I used to obtain u(x,y) = cos(√(y2-x2))
    (b) u(x=y,y)=y
    I am not quite sure how to approach this latter and would appreciate some advice.
  2. jcsd
  3. Dec 31, 2013 #2


    User Avatar
    Homework Helper

    The problem is not well-posed: you've shown that [itex]y = x[/itex] is a characteristic, so [itex]u[/itex] must be constant on [itex]y = x[/itex] and the value of [itex]u[/itex] on [itex]y = x[/itex] tells you nothing about the value of [itex]u[/itex] on [itex]x^2 - y^2 = \epsilon[/itex] for any [itex]\epsilon \neq 0[/itex].
  4. Dec 31, 2013 #3
    Pardon me, I did mean to add that. Indeed, if C=0 then, for y=+-x, u(x,y) = C. Otherwise (C different than zero), u(x,y)=x^2-y^2.
    I'd still appreciate your help with my problem :).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted