Question

Solution of laplace equation urr+ur(1/r)+upp(1/r^2)=0 outside the circle

Answer 1

Answer:

Find the solution u(r,θ)of Laplace's equation urr+(1/r)ur+(1/r2)uθθ=0 outside the circle r=a, that satisfies the boundary condition u(a,θ)=f(θ),0≤θ<2π,on the circle. Assume that u(r,θ)is single-valued and bounded for r>a.

Answer 2

Answer:

Find the solution u(r,θ)of Laplace's equation urr+(1/r)ur+(1/r2)uθθ=0 outside the circle r=a, that satisfies the boundary condition u(a,θ)=f(θ),0≤θ<2π,on the circle. Assume that u(r,θ)is single-valued and bounded for r>a.