Laplace PDE on Disk - Poisson's Formula

Partial Differential Equations
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Joined: Wed Nov 15, 2017 12:37 pm

Laplace PDE on Disk - Poisson's Formula


Post by andrew.tzeva »

After separating the variables, I ended up with a general solution of the form:
$$u(r,\theta)=\sum_{n=0}^{\infty} r^n[A_n\cos(n\theta)+B_nsin(n\theta)]$$
How exactly do I use the boundary condition $u(\alpha,\theta)=1+3\sin(\theta)$ to determine the coefficients? (I think I know the answer intuitively, but I would like to see how it can be presented in a more mathematically formal way)
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