Question

Boundary-Value Problems in Other Coordinate Systems

1. Solve ∆u = 0 in a disk x^2 + y^2 ≤ 25, where u(5, θ) = 7 sin 3θ − 6 sin 8θ and u is bounded when   r = 0.
2. Solve ∆u = 0 in an annulus 1 ≤ x^2+y^2 ≤ 4, where u(1, θ) = 75 sin θ, u(2, θ) = 60 cos θ.
3. Find the steady-state temperature distribution in a disk of radius 1 if the upper half of the circumference is kept at 100◦ and the lower half is kept at 0◦ .

Answer 1