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Using conform transformations to solve a Dirichlet problem with 3 border conditions

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a function H in C such that [tex]{\nabla ^2}H = 0[/tex] for y>0, H(0,y) = 1 for y<-[tex]/pi[/tex], H(0,y) = 0 for y>[tex]/pi[/tex] and H(0,y) = -1 for -[tex]/pi[/tex]<y<[tex]/pi[/tex].

    3. The attempt at a solution

    I haven't been able to came up with anything. All the conform transformations that I know allow me to solve the Dirichlet problem with only 2 conditions, or 3 but with two of them with the same value. I was told that I could just leave the geometry of the problem like it is (that is, not make any transformation) and propose the solution A[tex]\theta[/tex]1 + B[tex]\theta[/tex]2 + C, being [tex]\theta[/tex]1 the argument of [z - (0 -i*Pi)] and [tex]\theta[/tex]2 the argument of [z - (0 +i*Pi)], but the solution I find doesn't satisfy the border conditions.

    Any ideas?
     
  2. jcsd
  3. Nov 26, 2009 #2
    Re: Using conform transformations to solve a Dirichlet problem with 3 border conditio

    Nobody knows this?
     
  4. Nov 29, 2009 #3
    Re: Using conform transformations to solve a Dirichlet problem with 3 border conditio

    I leave a graphic of the problem.
    http://img692.imageshack.us/img692/333/asdasdxk.png [Broken]

    Does anybody know the answer? Because I kind of need it urgently...

    Thanks.
     
    Last edited by a moderator: May 4, 2017
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