Question

Determine the solution of the Laplace equation in polar coordinate subject to the following boundary conditions. frac{partial^2u}{partial r^2} + frac{1}{r} frac{partial u}{partial r} + frac{1}{r^2} frac{partial^2u}{partial heta^2} = 0, quad 0 < heta < frac{pi}{2}, quad 1 < r < 2, u(1, heta) = 1, quad u(2, heta) = 0, quad 0 < heta < frac{pi}{2} u(r,0) = 0, quad u(r,pi/2) = 0, quad 1 < r < 2.

          Determine the solution of the Laplace equation in polar coordinate subject to the following boundary conditions.

frac{partial^2u}{partial r^2} + frac{1}{r} frac{partial u}{partial r} + frac{1}{r^2} frac{partial^2u}{partial 	heta^2} = 0, quad 0 < 	heta < frac{pi}{2}, quad 1 < r < 2,

u(1,	heta) = 1, quad u(2,	heta) = 0, quad 0 < 	heta < frac{pi}{2}

u(r,0) = 0, quad u(r,pi/2) = 0, quad 1 < r < 2.

$Determine the solution of the Laplace equation in polar coordinate subject to the following boundary conditions. fracpartial^2upartial r^2 + frac1r fracpartial upartial r + frac1r^2 fracpartial^2upartial heta^2 = 0, quad 0 < heta < fracpi2, quad 1 < r < 2, u(1, heta) = 1, quad u(2, heta) = 0, quad 0 < heta < fracpi2 u(r,0) = 0, quad u(r,pi/2) = 0, quad 1 < r < 2.$

Added by Donald H.

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