Find a solution to the following Dirichlet problem for a
Chapter 10, Problem 15E(choose chapter or problem)
Find a solution to the following Dirichlet problem for a half disk:
\(\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{r} \frac{\partial u}{\partial r}+\frac{1}{r^{2}} \frac{\partial^{2} u}{\partial \theta^{2}}=0\),
\(0<r<1, \quad 0<\theta<\pi\),
\(u(r, 0)=0, \quad 0 \leq r \leq 1\),
\(u(r, 0)=0, \quad 0 \leq r \leq 1\),
\(u(1, \theta)=\sin 3 \theta, \quad 0 \leq \theta \leq \pi\),
\(u(0, \theta)\), bounded
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<r<1, 0<theta<pi
u(r,0)=0, 0leq r leq 1
u(r,pi)=0, 0 leq r leq 1
u(1,theta=sin 3theta, 0 leq theta leq pi
u(0,theta)
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