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PDE question.

  1. Dec 31, 2013 #1
    Hi,
    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

    pasmith

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    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 :).
     
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