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Unformatted text preview: , u ( r, θ, ϕ, 0) = f ( r, θ, ϕ ) ∂u ∂t ( r, θ, ϕ, 0) = 0 . 5.- (25 pts) (a) (15 pts) Solve ∇ 2 u = 0 for ρ < 1 , t > , ∂u ∂ρ = g ( θ, φ ) for ρ = 1 where the function g is assumed to satisfy Z 2 π Z π g ( θ, ϕ ) sin( θ ) dθdϕ = 0 . (1) Show that this problem admits a unique solution up to an additive constant, that can be determined if, for example, we assume the temperature scale is such that u = 0 at ρ = 0 for t = 0. (b) (10 pts) What happens if the integral in (1) is not zero? Compare with problem 1.: no special conditions on the boundary values were needed there. Explain! Due April 30, 3:00pm....
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- Spring '09
- pts, Boundary value problem, Normal mode