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Laplace equation in polar coordinate

  1. Nov 14, 2008 #1
    Urr+(1/r)*Ur+(1/r^2)*Uθθ=0

    a<r<b, 0<θ<w

    with the conditions
    U(r,0)=U1
    U(r,w)=U2
    U(a,θ)=0
    U(b,θ)=f(θ)
     
  2. jcsd
  3. Nov 15, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi NapoleonZ! Welcome to PF! :smile:
    Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
     
  4. Nov 15, 2008 #3
    I have got two sets of solutions

    U(r,θ)=A*ln(r)+B*
    U(r,θ)=(C*r^λ+D/r^λ)*(E*sinλθ+F*cosλθ)

    My problem is the boundary conditions are nonhomogeneous, with which I cannot work out the coefficients.
     
  5. Nov 15, 2008 #4

    tiny-tim

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    Hi NapoleonZ! :smile:

    i] I'm a little confused about the conditions … U(a,θ)=0 seems incompatible with U(r,0)=U1
    and U(r,w)=U2, if the conditions are continuous

    ii] Doesn't the condition U(a,θ)=0 make it fairly clear what E and F are (unless λ = 0)?
     
  6. Nov 15, 2008 #5

    i] I'm confused too.
    ii] No always, actually D=-C*a^(2n)
     
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