In 7 and 8, find a solution to the Dirichlet boundary
Chapter 10, Problem 7E(choose chapter or problem)
In Problems 7 and 8, find a solution to the Dirichlet boundary value problem for a disk:
\(\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{r} \frac{\partial u}{\partial r}+\frac{1}{r^{2}} \frac{\partial^{2} u}{\partial \theta^{2}}=0\)
\(0 \leq r<2, \quad-\pi \leq \theta \leq \pi\)
\(u(2, \theta)=f(\theta), \quad-\pi \leq \theta \leq \pi\)
for the given function \(f(\theta)\).
\(f(\theta)=|\theta|, \quad-\pi \leq \theta \leq \pi\)
Equation Transcription:
Text Transcription:
\partial^2 u \partial r^2+1 r \partial un\partial r+1 r^2 \partial^2 u\partial \theta^{2}}=0
0 \leq r<2, \quad-\pi \leq \theta \leq \pi
u(2, \theta)=f(\theta), \quad-\pi \leq \theta \leq \pi
f(\theta)
f(\theta)=|\theta|, \quad-\pi \leq \theta \leq \pi
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