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Boundary problem

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    We are given the pde:
    [tex]\partial^2{v}/\partial{r^2}[/tex]+(1/r)[tex]\partial{v}/\partial{r}[/tex]+(1/r^2)[tex]\partial^2{v}/\partial{\theta^2}[/tex]=0
    and we are given that a general solution is given by:
    v(r,[tex]\theta[/tex])=A[tex]_{0}[/tex]+B[tex]_{0}[/tex]ln(r) + [tex]\sum{r^{n}(A_{n}cos(n\theta) + B_{n}sin(n\theta))}+\sum{(1/r^n)(C_{n}cos(n\theta)+D_{n}sin(n\theta))}[/tex]

    show that if [tex]\Omega[/tex] is a disk centered at the origin of radius r0, continuous solutions of the pde are of the type:
    v(r,[tex]\theta[/tex])=A0+[tex]\sum{r^n(A_{n}cos(n\theta)+B_{n}sin(n\theta))}[/tex]


    2. Relevant equations



    3. The attempt at a solution
    i think we have to show that \sum{(1/r^n)(C_{n}cos(n\theta)+D_{n}sin(n\theta))}[/tex] and B0ln(r) are not continuous but i dont think thats right.
    Any help would be very much appreciated.
     
    Last edited: Mar 29, 2009
  2. jcsd
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