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Please help is solving the non homogeneous heat problem.

  1. May 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Find solution of a nonhomogeneous heat problem:

    [tex] \frac{\partial U}{\partial t} = c^2( \frac{\partial^2 U}{\partial r^2} + \frac{1}{r}\frac{\partial U}{\partial r} + \frac{1}{r^2}\frac{\partial^2 U}{\partial \theta^2} + g(r,\theta,t) [/tex]

    With boundary condition: [itex] U(a,\theta, t) = 0 [/itex]

    Initial condition: [itex] U(r,\theta,0) = f(r,\theta)[/itex]

    2. The attempt at a solution 1

    The associate homogeneous equation is:

    [tex] U(r,\theta,t)=R\Theta T \;\;\;\;\Rightarrow\;\;\;\; R\Theta T' + c^2(R''\Theta T + \frac{1}{r}R'\Theta T + \frac{1}{r^2}R\Theta'' T)= g(r,\theta,t)[/tex]

    Where [tex] U_c(r,\theta,t) = \sum_{m=0}^{\infty}\sum_{n=1}^{\infty}J_m(\lambda_{mn}r)[A_{mn}cos(m\theta) + B_{mn} sin(m\theta)]e^{-c^2\lambda^2_{mn}t}[/tex]

    I don't know how to solve for particular solution.
    Last edited: May 18, 2010
  2. jcsd
  3. May 19, 2010 #2
    Anyone please? I just want some guidance how to approach this problem.
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