Find a solution to the Neumann boundary value problem for
Chapter 10, Problem 9E(choose chapter or problem)
Find a solution to the Neumann boundary value problem for a disk:
\(\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{r} \frac{\partial u}{\partial r}+\frac{1}{r^{2}} \frac{\partial^{2} u}{\partial \theta^{2}}=0\)
\(0 \leq r<a, \quad-\pi \leq \theta \leq \pi\)
\(\frac{\partial u}{\partial r}(a, \theta)=f(\theta),-\pi \leq \theta \leq \pi\)
Equation Transcription:
Text Transcription:
\partial^2 u\partial r^2+1 r \partial u \partial r+1 r^2 \partial^2 u\partial \theta^2=0
0 \leq r<a, \quad-\pi \leq \theta \leq \pi
\partial u \partial r(a, \theta)=f(\theta),-\pi \leq \theta \leq \pi
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